statement stringlengths 1 374 | proof stringlengths 0 1.98k | type stringclasses 14
values | symbolic_name stringlengths 1 50 | library stringclasses 1
value | filename stringclasses 3
values | imports listlengths 14 19 | deps listlengths 0 21 | docstring stringclasses 27
values | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
PredType : forall T pT, (pT -> pred T) -> predType T. | exact PredType || exact mkPredType.
Defined. | Definition | PredType | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | Copy of the ssrbool shim to ensure compatibility with MathComp v1.8.0. | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 |
predOfType T | := (pred_of_simpl (@pred_of_argType T)). | Notation | predOfType | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
oextract (T : Type) (o : option T) : o -> T | :=
if o is Some t return o -> T then fun=> t else False_rect T \o notF. | Definition | oextract | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
oextractE (T : Type) (x : T) (xP : Some x) : oextract xP = x. | Proof. by []. Qed. | Lemma | oextractE | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"oextract"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
Some_oextract T (x : option T) (x_ex : x) : Some (oextract x_ex) = x. | Proof. by case: x x_ex. Qed. | Lemma | Some_oextract | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"oextract"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
ojoin T (x : option (option T)) | :=
if x is Some y then y else None. | Definition | ojoin | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
Some_ojoin T (x : option (option T)) : x -> Some (ojoin x) = x. | Proof. by case : x. Qed. | Lemma | Some_ojoin | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"ojoin"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
ojoinT T (x : option (option T)) : ojoin x -> x. | Proof. by case: x. Qed. | Lemma | ojoinT | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"ojoin"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
TaggedP (T1 : Type) (T2 : T1 -> Type) (P : forall x, T2 x -> Type) :
(forall t : {x : T1 & T2 x}, P _ (tagged t)) ->
forall (x : T1) (y : T2 x), P x y. | Proof. by move=> /(_ (Tagged _ _)). Qed. | Lemma | TaggedP | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
f : seq K -> seq K. | Axiom | f | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | ||
perm : forall s, perm_eq (f s) (undup s). | Axiom | perm | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | ||
uniq : forall s, uniq (f s). | Axiom | uniq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | ||
E : forall (s : seq K), f s =i s. | Axiom | E | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | ||
eq : forall (s s' : seq K), s =i s' <-> f s = f s'. | Axiom | eq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | ||
f (s : seq K) | := choose (perm_eq (undup s)) (undup s). | Definition | f | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
perm s : perm_eq (f s) (undup s). | Proof. by rewrite perm_sym chooseP. Qed. | Fact | perm | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
uniq s : uniq (f s). | Proof. by rewrite (perm_uniq (perm _)) undup_uniq. Qed. | Fact | uniq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"perm"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
E (s : seq K) : f s =i s. | Proof. by move=> x; rewrite (perm_mem (perm _)) mem_undup. Qed. | Fact | E | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"perm"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
eq (s s' : seq K) : s =i s' <-> f s = f s'. | Proof.
split=> [eq_ss'|eq_ss' k]; last by rewrite -E eq_ss' E.
rewrite /f; have peq_ss' : perm_eq (undup s) (undup s').
by apply: uniq_perm; rewrite ?undup_uniq // => x; rewrite !mem_undup.
rewrite (@choose_id _ _ _ (undup s')) //=; apply: eq_choose => x /=.
by apply: sym_left_transitive; [exact: perm_sym | exact: (@... | Lemma | eq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
sort_keys | := SortKeys.f. | Notation | sort_keys | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
sort_keys_perm | := SortKeys.perm. | Notation | sort_keys_perm | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"perm"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
sort_keys_uniq | := SortKeys.uniq. | Notation | sort_keys_uniq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
sort_keysE | := SortKeys.E. | Notation | sort_keysE | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
eq_sort_keys | := SortKeys.eq. | Notation | eq_sort_keys | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"eq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
mem_sort_keys ks k : k \in ks -> k \in sort_keys ks. | Proof. by rewrite sort_keysE. Qed. | Lemma | mem_sort_keys | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"sort_keys",
"sort_keysE"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
mem_sort_keys_intro ks k : k \in sort_keys ks -> k \in ks. | Proof. by rewrite sort_keysE. Qed. | Lemma | mem_sort_keys_intro | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"sort_keys",
"sort_keysE"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
sort_keys_nil : sort_keys [::] = [::] :> seq K. | Proof.
have := sort_keysE ([::] : seq K).
by case: sort_keys => //= a l /(_ a); rewrite mem_head.
Qed. | Lemma | sort_keys_nil | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"sort_keys",
"sort_keysE"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
sort_keys_id ks : sort_keys (sort_keys ks) = sort_keys ks. | Proof. by have /eq_sort_keys := sort_keysE ks. Qed. | Lemma | sort_keys_id | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"eq_sort_keys",
"sort_keys",
"sort_keysE"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
canonical_keys ks | := sort_keys ks == ks. | Definition | canonical_keys | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"sort_keys"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
canonical_uniq ks : canonical_keys ks -> uniq ks. | Proof. by move=> /eqP <-; exact: sort_keys_uniq. Qed. | Lemma | canonical_uniq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"canonical_keys",
"sort_keys_uniq",
"uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
canonical_sort_keys ks : canonical_keys (sort_keys ks). | Proof. by rewrite /canonical_keys sort_keys_id. Qed. | Lemma | canonical_sort_keys | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"canonical_keys",
"sort_keys",
"sort_keys_id"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
canonical_eq_keys ks ks' :
canonical_keys ks -> canonical_keys ks' ->
ks =i ks' -> ks = ks'. | Proof.
move=> /eqP; case: _ /; move=> /eqP; case: _ / => eq_ks_ks'.
by apply/eq_sort_keys => x; rewrite -sort_keysE eq_ks_ks' sort_keysE.
Qed. | Lemma | canonical_eq_keys | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"canonical_keys",
"eq_sort_keys",
"sort_keysE"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
size_sort_keys ks : size (sort_keys ks) = size (undup ks). | Proof. exact: perm_size. Qed. | Lemma | size_sort_keys | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"sort_keys"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
finSet : Type | := mkFinSet {
enum_fset :> seq K;
_ : canonical_keys enum_fset
}. | Structure | finSet | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"canonical_keys"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
finset_of (_ : phant K) | := finSet. | Definition | finset_of | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finSet"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
"{fset T }" | := (finSet T) : type_scope. | Notation | {fset T } | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finSet"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
pred_of_finset (K : choiceType)
(f : finSet K) : pred K | := fun k => k \in (enum_fset f). | Definition | pred_of_finset | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finSet"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
finSetPredType (K : choiceType) | := PredType (@pred_of_finset K). | Canonical | finSetPredType | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"PredType",
"pred_of_finset"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
keys_canonical : canonical_keys (enum_fset A). | Proof. by case: A. Qed. | Lemma | keys_canonical | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"canonical_keys"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fset_uniq : uniq (enum_fset A). | Proof. by rewrite canonical_uniq // keys_canonical. Qed. | Lemma | fset_uniq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"canonical_uniq",
"keys_canonical",
"uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fset_sub_type : predArgType | :=
FSetSub {fsval : K; fsvalP : in_mem fsval (@mem K _ A)}. | Record | fset_sub_type | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fset_sub_enum : seq fset_sub_type | :=
undup (pmap insub (enum_fset A)). | Definition | fset_sub_enum | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"fset_sub_type"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
mem_fset_sub_enum x : x \in fset_sub_enum. | Proof. by rewrite mem_undup mem_pmap -valK map_f // fsvalP. Qed. | Lemma | mem_fset_sub_enum | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"fset_sub_enum"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
val_fset_sub_enum : map val fset_sub_enum = enum_fset A. | Proof.
rewrite /fset_sub_enum undup_id ?pmap_sub_uniq ?fset_uniq//.
rewrite (pmap_filter (@insubK _ _ _)); apply/all_filterP.
by apply/allP => x; rewrite isSome_insub.
Qed. | Lemma | val_fset_sub_enum | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"fset_sub_enum",
"fset_uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fset_sub_pickle x | := index x fset_sub_enum. | Definition | fset_sub_pickle | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"fset_sub_enum"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fset_sub_unpickle n | := nth None (map some fset_sub_enum) n. | Definition | fset_sub_unpickle | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"fset_sub_enum"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fset_sub_pickleK : pcancel fset_sub_pickle fset_sub_unpickle. | Proof.
rewrite /fset_sub_unpickle => x.
by rewrite (nth_map x) ?nth_index ?index_mem ?mem_fset_sub_enum.
Qed. | Lemma | fset_sub_pickleK | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"fset_sub_pickle",
"fset_sub_unpickle",
"mem_fset_sub_enum"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
enum_fsetE : enum_fset A = [seq val i | i <- enum fset_sub_type]. | Proof. by rewrite enumT unlock val_fset_sub_enum. Qed. | Lemma | enum_fsetE | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"fset_sub_type",
"val_fset_sub_enum"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
cardfE : size (enum_fset A) = #|fset_sub_type|. | Proof. by rewrite cardE enum_fsetE size_map. Qed. | Lemma | cardfE | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"enum_fsetE",
"fset_sub_type"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fset_sub_type : finSet >-> predArgType. | Coercion | fset_sub_type | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finSet"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | ||
"[` kf ]" | := (FSetSub kf) (format "[` kf ]") : fset_scope. | Notation | [` kf ] | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fsetsubE (T : choiceType) (A : {fset T}) (x : A) (xA : val x \in A) :
[` xA] = x. | Proof. by apply/val_inj => /=. Qed. | Lemma | fsetsubE | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
"#|` A |" | := (size (enum_fset A))
(at level 0, A at level 99, format "#|` A |") : nat_scope. | Notation | #|` A | | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fset_predT {T : choiceType} {A : {fset T}} : simpl_pred A | := @predT A. | Definition | fset_predT | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
set_of_fset (K : choiceType) (A : {fset K}) : {set A} | :=
[set x in {: A}]. | Definition | set_of_fset | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
seq_fset | := (seq_fset finset_key). | Notation | seq_fset | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
seq_fsetE : seq_fset s =i s. | Proof. by move=> a; rewrite unlock sort_keysE. Qed. | Lemma | seq_fsetE | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"seq_fset",
"sort_keysE"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
size_seq_fset : size (seq_fset s) = size (undup s). | Proof. by rewrite unlock /= size_sort_keys. Qed. | Lemma | size_seq_fset | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"seq_fset",
"size_sort_keys"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
seq_fset_uniq : uniq (seq_fset s). | Proof. by rewrite unlock /= sort_keys_uniq. Qed. | Lemma | seq_fset_uniq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"seq_fset",
"sort_keys_uniq",
"uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
seq_fset_perm : perm_eq (seq_fset s) (undup s). | Proof. by rewrite unlock //= sort_keys_perm. Qed. | Lemma | seq_fset_perm | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"seq_fset",
"sort_keys_perm"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
finpredType (T : eqType) | := FinPredType {
finpred_sort :> Type;
tofinpred : finpred_sort -> pred T;
_ : {finpred_seq : finpred_sort -> seq T |
((forall p, uniq (finpred_seq p))
* forall p x, x \in finpred_seq p = tofinpred p x)%type}
}. | Structure | finpredType | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
finpredType_predType (T : eqType) (fpT : finpredType T) | :=
@PredType T (finpred_sort fpT) (@tofinpred T fpT). | Canonical | finpredType_predType | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"PredType",
"finpredType"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
enum_finpred (T : eqType) (fpT : finpredType T) :
fpT -> seq T | :=
let: FinPredType _ _ (exist s _) := fpT in s. | Definition | enum_finpred | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finpredType"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
enum_finpred_uniq (T : eqType) (fpT : finpredType T) (p : fpT) :
uniq (enum_finpred p). | Proof. by case: fpT p => ?? [s sE] p; rewrite sE. Qed. | Lemma | enum_finpred_uniq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"enum_finpred",
"finpredType",
"uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
enum_finpredE (T : eqType) (fpT : finpredType T) (p : fpT) :
enum_finpred p =i p. | Proof. by case: fpT p => ?? [s sE] p x; rewrite sE -topredE. Qed. | Lemma | enum_finpredE | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"enum_finpred",
"finpredType"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
mkFinPredType_of_subproof (T : eqType) (pT : predType T)
(fpred_seq : pT -> seq T) (pred_fsetE : forall p, fpred_seq p =i p) :
forall p x, x \in fpred_seq p = topred p x. | Proof. by move=> p x; rewrite topredE pred_fsetE. Qed. | Lemma | mkFinPredType_of_subproof | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
mkFinPredType_of (T : eqType) (U : Type) | :=
fun (pT : predType T) & pred_sort pT -> U =>
fun a (pT' := @PredType T U a) & phant_id pT' pT =>
fun (fpred_seq : pT' -> seq T)
(fpred_seq_uniq : forall p, uniq (fpred_seq p))
(fpred_seqE : forall p, fpred_seq p =i p) =>
@FinPredType T U a (exist _ fpred_seq
(fpred_seq_uniq, (mkFinPredType_of_... | Definition | mkFinPredType_of | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"PredType",
"mkFinPredType_of_subproof",
"uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
clone_finpredType (T : eqType) (U : Type) | :=
fun (pT : finpredType T) & finpred_sort pT -> U =>
fun a pP (pT' := @FinPredType T U a pP) & phant_id pT' pT => pT'. | Definition | clone_finpredType | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finpredType"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
is_finite (T : eqType) (P : pred T) | := IsFinite {
seq_of_is_finite :> seq T;
_ : uniq seq_of_is_finite;
_ : forall x, x \in seq_of_is_finite = P x;
}. | Structure | is_finite | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
is_finite_uniq (T : eqType) (P : pred T) (p : is_finite P) : uniq p. | Proof. by case: p. Qed. | Lemma | is_finite_uniq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"is_finite",
"uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
is_finiteE (T : eqType) (P : pred T) (p : is_finite P) x :
x \in (seq_of_is_finite p) = P x. | Proof. by case: p. Qed. | Lemma | is_finiteE | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"is_finite"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
finpred (T : eqType) (pT : predType T) | := FinPred {
pred_of_finpred :> pT;
_ : is_finite [pred x in pred_of_finpred]
}. | Structure | finpred | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"is_finite"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
enum_fin (T : eqType) (pT : predType T) (p : finpred pT) : seq T | :=
let: FinPred _ fp := p in fp. | Definition | enum_fin | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finpred"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
enum_fin_uniq (T : eqType) (pT : predType T) (p : finpred pT) :
uniq (enum_fin p). | Proof. by case: p => ?[]. Qed. | Lemma | enum_fin_uniq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"enum_fin",
"finpred",
"uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
enum_finE (T : eqType) (pT : predType T) (p : finpred pT) :
enum_fin p =i (pred_of_finpred p). | Proof. by case: p => ?[]. Qed. | Lemma | enum_finE | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"enum_fin",
"finpred"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fin_finpred (T : eqType) (pT : finpredType T) (p : pT) | :=
@FinPred _ _ p (@IsFinite _ _ (enum_finpred p)
(enum_finpred_uniq p) (enum_finpredE p)). | Canonical | fin_finpred | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"enum_finpred",
"enum_finpredE",
"enum_finpred_uniq",
"finpredType"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
finpred_of (T : eqType) (pT : predType T) (p : pT)
(fp : finpred pT) & phantom pT fp : finpred pT | := fp. | Definition | finpred_of | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finpred"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
finmempred (T : eqType) | := FinMemPred {
pred_of_finmempred :> mem_pred T;
_ : is_finite (fun x => in_mem x pred_of_finmempred)
}. | Structure | finmempred | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"is_finite"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
enum_finmem (T : eqType) (p : finmempred T) : seq T | :=
let: FinMemPred _ fp := p in fp. | Definition | enum_finmem | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finmempred"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
enum_finmem_uniq (T : eqType) (p : finmempred T) :
uniq (enum_finmem p). | Proof. by case: p => ?[]. Qed. | Lemma | enum_finmem_uniq | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"enum_finmem",
"finmempred",
"uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
enum_finmemE (T : eqType) (p : finmempred T) :
enum_finmem p =i p. | Proof. by case: p => ?[]. Qed. | Lemma | enum_finmemE | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"enum_finmem",
"finmempred"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
finmempred_of (T : eqType) (P : pred T)
(mP : finmempred T) & phantom (mem_pred T) mP : finmempred T | := mP. | Definition | finmempred_of | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finmempred"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
mem_fin (T : eqType) (pT : predType T) (p : finpred pT) | :=
@FinMemPred _ (mem p)
(@IsFinite _ _ (enum_fin p) (enum_fin_uniq p) (enum_finE p)). | Canonical | mem_fin | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"enum_fin",
"enum_finE",
"enum_fin_uniq",
"finpred"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
"[ 'finpredType' 'of' T ]" | := (@clone_finpredType _ T _ id _ _ id)
(at level 0, format "[ 'finpredType' 'of' T ]") : form_scope. | Notation | [ 'finpredType' 'of' T ] | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"clone_finpredType"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
mkFinPredType T s s_uniq sE | :=
(@mkFinPredType_of _ T _ id _ id s s_uniq sE). | Notation | mkFinPredType | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"mkFinPredType_of"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fset_finpredType (T: choiceType) | :=
mkFinPredType (finSet T) (@enum_fset T) (@fset_uniq T) (fun _ _ => erefl). | Canonical | fset_finpredType | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finSet",
"fset_uniq",
"mkFinPredType"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
pred_finpredType (T : finType) | :=
mkFinPredType (pred T) (fun P => enum_mem (mem P)) (@enum_uniq T) (@mem_enum T). | Canonical | pred_finpredType | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"mkFinPredType"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
simpl_pred_finpredType (T : finType) | :=
mkFinPredType (simpl_pred T) (fun P => enum_mem (mem P)) (@enum_uniq T) (@mem_enum T). | Canonical | simpl_pred_finpredType | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"mkFinPredType"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
fset_finpred (T: choiceType) (A : finSet T) | :=
@FinPred _ _ (enum_fset A)
(@IsFinite _ _ (enum_fset A) (fset_uniq _) (fun=> erefl)). | Canonical | fset_finpred | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"finSet",
"fset_uniq"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
subfinset_finpred (T : choiceType)
(A : finmempred T) (Q : pred T) | :=
@FinPred _ _ [pred x in A | Q x]
(@IsFinite _ _ [seq x <- enum_finmem A | Q x] _ _). | Canonical | subfinset_finpred | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"enum_finmem",
"finmempred"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
seq_finpredType (T : eqType) | :=
mkFinPredType (seq T) undup (@undup_uniq T) (@mem_undup T). | Canonical | seq_finpredType | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"mkFinPredType"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
imfset | := imfset. | Notation | imfset | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
imfset2 | := imfset2. | Notation | imfset2 | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
"A `=` B" | := (A = B :> {fset _}) (only parsing) : fset_scope. | Notation | A `=` B | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
"A `<>` B" | := (A <> B :> {fset _}) (only parsing) : fset_scope. | Notation | A `<>` B | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
"A `==` B" | := (A == B :> {fset _}) (only parsing) : fset_scope. | Notation | A `==` B | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
"A `!=` B" | := (A != B :> {fset _}) (only parsing) : fset_scope. | Notation | A `!=` B | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
"A `=P` B" | := (A =P B :> {fset _}) (only parsing) : fset_scope. | Notation | A `=P` B | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
"f @`[ key ] A" | := (imfset key f (mem A)) : fset_scope. | Notation | f @`[ key ] A | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"imfset"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 | |
"f @2`[ key ] ( A , B )" | :=
(imfset2 key f (mem A) (fun x => (mem (B x)))) : fset_scope. | Notation | f @2`[ key ] ( A , B ) | Root | finmap.v | [
"Corelib",
"Setoid",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrnat",
"eqtype",
"ssrfun",
"seq",
"choice",
"finset",
"finfun",
"fintype",
"bigop",
"Prenex",
"Implicits",
"Monoid"
] | [
"imfset2"
] | https://github.com/math-comp/finmap | 53239c7997b1143592d7814ec51a0e3404844b54 |
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