statement stringlengths 1 4.33k | proof stringlengths 0 37.9k | type stringclasses 25
values | symbolic_name stringlengths 1 67 | library stringclasses 10
values | filename stringclasses 112
values | imports listlengths 2 138 | deps listlengths 0 64 | docstring stringclasses 798
values | source_url stringclasses 1
value | commit stringclasses 1
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|---|---|---|---|---|---|---|---|---|---|---|
test_eq_bool x : (x <= 2) = (-x >= -2). | Proof. lra. Qed. | Lemma | test_eq_bool | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_not x : x <= 2 -> ~ (x > 2). | Proof. lra. Qed. | Lemma | test_not | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_negb x : x <= 2 -> ~~ (x > 2). | Proof. lra. Qed. | Lemma | test_negb | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_and x : x <= 2 -> (x <= 3 /\ x <= 4). | Proof. lra. Qed. | Lemma | test_and | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_andb x : x <= 2 -> (x <= 3) && (x <= 4). | Proof. lra. Qed. | Lemma | test_andb | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_or x : x <= 2 -> (x <= 3 \/ x <= 1). | Proof. lra. Qed. | Lemma | test_or | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_orb x : x <= 2 -> (x <= 3) || (x <= 1). | Proof. lra. Qed. | Lemma | test_orb | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_exfalso x (xle2 : x <= 2) (xge3 : x >= 3) : bool. | Proof. lra. Qed. | Lemma | test_exfalso | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_rat_constant x : 0 <= x -> 1 / 3 * x <= 2^-1 * x. | Proof. lra. Qed. | Lemma | test_rat_constant | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_rfstr (x : rat) : (x <= 2) || true = true. | Proof. lra. Qed. | Lemma | test_rfstr | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [
"rat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
plus_minus x y : 0 = x + y -> 0 = x - y -> 0 = x /\ 0 = y. | Proof. lra. Qed. | Lemma | plus_minus | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
plus_minus' x y : 0 = x + y -> 0 = x - y -> 0 = x /\ 0 = y. | Proof. move=> *; lra. Qed. | Lemma | plus_minus' | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
cst_test : 5^+5 = 5 * 5 * 5 * 5 * 5 :> F. | Proof. lra. Qed. | Lemma | cst_test | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
binomial x y : (x + y)^+2 = x^+2 + 2 * x * y + y^+2. | Proof. move=> *; lra. Qed. | Lemma | binomial | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
hol_light19 x y : 2 * y + x = (x + y) + y. | Proof. lra. Qed. | Lemma | hol_light19 | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
vcgen_25 (n m jt j it i : F) :
1 * it - 2 * i - 1 = 0 ->
1 * jt - 2 * j - 1 = 0 ->
1 * n - 10 = 0 ->
0 <= -(4028%:R) * i + 6222%:R * j + 705 * m + -(16674%:R) ->
0 <= - 418 * i + 651 * j + 94 * m + -(1866%:R) ->
0 <= - 209 * i + 302 * j + 47 * m - 839 ->
0 <= - 1 * i + 1 * j - 1 ->
0 <= - 1 * j + 1 * m... | Proof. move=> *; lra. Qed. | Lemma | vcgen_25 | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
l1 x y z : `|x - z| <= `|x - y| + `|y - z|. | Proof.
Fail intros; split_Rabs; lra. (* TODO should work *)
Abort. | Lemma | l1 | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
l2 x y :
x < `|y| -> y < 1 -> x >= 0 -> - y <= 1 -> `|x| <= 1. | Proof.
Fail intros; split_Rabs; lra. (* TODO should work *)
Abort. | Lemma | l2 | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
opp_eq_0_iff x : -x = 0 <-> x = 0. | Proof. lra. Qed. | Lemma | opp_eq_0_iff | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | Bug 5073 | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
motzkin' x y :
(x^+2 + y^+2 + 1) * (x^+2 * y^+4 + x^+4*y^+2 + 1 - 3 * x^+2 * y^+2) >= 0. | Proof.
move=> *.
(* Requires CSDP *)
(* psatz 3. *)
(* Qed. *)
Abort. | Lemma | motzkin' | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_abstract_rmorphism (R : realDomainType) (f : {rmorphism R -> R})
(x y : R) : f y >= 0 -> f x + 2 * f (y + 1) <= f (3 * y + x) + 2. | Proof. lra. Qed. | Example | test_abstract_rmorphism | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_concrete_rmorphism (R : realFieldType) (x y : rat) :
ratr y >= 0 :> R -> ratr x + 2 * ratr (y + 1) <= ratr (3 * y + x) + 2 :> R. | Proof. lra. Qed. | Example | test_concrete_rmorphism | test_suite | test_suite/test_lra.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"arithmetic_tactic"
] | [
"rat",
"ratr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_preorderType (T : preorderType disp) :
Order.Preorder.on T = Order.Preorder.on T^d^d | := erefl. | Let | eq_dual_dual_preorderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_porderType (T : porderType disp) :
Order.POrder.on T = Order.POrder.on T^d^d | := erefl. | Let | eq_dual_dual_porderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_bPOrderType (T : bPOrderType disp) :
Order.BPOrder.on T = Order.BPOrder.on T^d^d | := erefl. | Let | eq_dual_dual_bPOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tPOrderType (T : tPOrderType disp) :
Order.TPOrder.on T = Order.TPOrder.on T^d^d | := erefl. | Let | eq_dual_dual_tPOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tbPOrderType (T : tbPOrderType disp) :
Order.TBPOrder.on T = Order.TBPOrder.on T^d^d | := erefl. | Let | eq_dual_dual_tbPOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_meetSemilatticeType (T : meetSemilatticeType disp) :
Order.MeetSemilattice.on T = Order.MeetSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_meetSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_bMeetSemilatticeType (T : bMeetSemilatticeType disp) :
Order.BMeetSemilattice.on T = Order.BMeetSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_bMeetSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tMeetSemilatticeType (T : tMeetSemilatticeType disp) :
Order.TMeetSemilattice.on T = Order.TMeetSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_tMeetSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tbMeetSemilatticeType (T : tbMeetSemilatticeType disp) :
Order.TBMeetSemilattice.on T = Order.TBMeetSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_tbMeetSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_joinSemilatticeType (T : joinSemilatticeType disp) :
Order.JoinSemilattice.on T = Order.JoinSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_joinSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_bJoinSemilatticeType (T : bJoinSemilatticeType disp) :
Order.BJoinSemilattice.on T = Order.BJoinSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_bJoinSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tJoinSemilatticeType (T : tJoinSemilatticeType disp) :
Order.TJoinSemilattice.on T = Order.TJoinSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_tJoinSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tbJoinSemilatticeType (T : tbJoinSemilatticeType disp) :
Order.TBJoinSemilattice.on T = Order.TBJoinSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_tbJoinSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_latticeType (T : latticeType disp) :
Order.Lattice.on T = Order.Lattice.on T^d^d | := erefl. | Let | eq_dual_dual_latticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_bLatticeType (T : bLatticeType disp) :
Order.BLattice.on T = Order.BLattice.on T^d^d | := erefl. | Let | eq_dual_dual_bLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tLatticeType (T : tLatticeType disp) :
Order.TLattice.on T = Order.TLattice.on T^d^d | := erefl. | Let | eq_dual_dual_tLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tbLatticeType (T : tbLatticeType disp) :
Order.TBLattice.on T = Order.TBLattice.on T^d^d | := erefl. | Let | eq_dual_dual_tbLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_distrLatticeType (T : distrLatticeType disp) :
Order.DistrLattice.on T = Order.DistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_distrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_bDistrLatticeType (T : bDistrLatticeType disp) :
Order.BDistrLattice.on T = Order.BDistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_bDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tDistrLatticeType (T : tDistrLatticeType disp) :
Order.TDistrLattice.on T = Order.TDistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_tDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tbDistrLatticeType (T : tbDistrLatticeType disp) :
Order.TBDistrLattice.on T = Order.TBDistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_tbDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_cDistrLatticeType (T : cDistrLatticeType disp) :
Order.CDistrLattice.on T = Order.CDistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_cDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_cbDistrLatticeType (T : cbDistrLatticeType disp) :
Order.CBDistrLattice.on T = Order.CBDistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_cbDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_ctDistrLatticeType (T : ctDistrLatticeType disp) :
Order.CTDistrLattice.on T = Order.CTDistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_ctDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_ctbDistrLatticeType (T : ctbDistrLatticeType disp) :
Order.CTBDistrLattice.on T = Order.CTBDistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_ctbDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_orderType (T : orderType disp) :
Order.Total.on T = Order.Total.on T^d^d | := erefl. | Let | eq_dual_dual_orderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_bOrderType (T : bOrderType disp) :
Order.BTotal.on T = Order.BTotal.on T^d^d | := erefl. | Let | eq_dual_dual_bOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tOrderType (T : tOrderType disp) :
Order.TTotal.on T = Order.TTotal.on T^d^d | := erefl. | Let | eq_dual_dual_tOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_tbOrderType (T : tbOrderType disp) :
Order.TBTotal.on T = Order.TBTotal.on T^d^d | := erefl. | Let | eq_dual_dual_tbOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finPOrderType (T : finPOrderType disp) :
Order.FinPOrder.on T = Order.FinPOrder.on T^d^d | := erefl. | Let | eq_dual_dual_finPOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finBPOrderType (T : finBPOrderType disp) :
Order.FinBPOrder.on T = Order.FinBPOrder.on T^d^d | := erefl. | Let | eq_dual_dual_finBPOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finTPOrderType (T : finTPOrderType disp) :
Order.FinTPOrder.on T = Order.FinTPOrder.on T^d^d | := erefl. | Let | eq_dual_dual_finTPOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finTBPOrderType (T : finTBPOrderType disp) :
Order.FinTBPOrder.on T = Order.FinTBPOrder.on T^d^d | := erefl. | Let | eq_dual_dual_finTBPOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finMeetSemilatticeType (T : finMeetSemilatticeType disp) :
Order.FinMeetSemilattice.on T = Order.FinMeetSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_finMeetSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finBMeetSemilatticeType (T : finBMeetSemilatticeType disp) :
Order.FinBMeetSemilattice.on T = Order.FinBMeetSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_finBMeetSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finJoinSemilatticeType (T : finJoinSemilatticeType disp) :
Order.FinJoinSemilattice.on T = Order.FinJoinSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_finJoinSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finTJoinSemilatticeType (T : finTJoinSemilatticeType disp) :
Order.FinTJoinSemilattice.on T = Order.FinTJoinSemilattice.on T^d^d | := erefl. | Let | eq_dual_dual_finTJoinSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_FinLatticeType (T : finLatticeType disp) :
Order.FinLattice.on T = Order.FinLattice.on T^d^d | := erefl. | Let | eq_dual_dual_FinLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_FinTBLatticeType (T : finTBLatticeType disp) :
Order.FinTBLattice.on T = Order.FinTBLattice.on T^d^d | := erefl. | Let | eq_dual_dual_FinTBLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_FinDistrLatticeType (T : finDistrLatticeType disp) :
Order.FinDistrLattice.on T = Order.FinDistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_FinDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_FinTBDistrLatticeType (T : finTBDistrLatticeType disp) :
Order.FinTBDistrLattice.on T = Order.FinTBDistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_FinTBDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finCDistrLatticeType (T : finCDistrLatticeType disp) :
Order.FinCDistrLattice.on T = Order.FinCDistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_finCDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finCTBDistrLatticeType (T : finCTBDistrLatticeType disp) :
Order.FinCTBDistrLattice.on T = Order.FinCTBDistrLattice.on T^d^d | := erefl. | Let | eq_dual_dual_finCTBDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finOrderType (T : finOrderType disp) :
Order.FinTotal.on T = Order.FinTotal.on T^d^d | := erefl. | Let | eq_dual_dual_finOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_dual_finTBOrderType (T : finTBOrderType disp) :
Order.FinTBTotal.on T = Order.FinTBTotal.on T^d^d | := erefl. | Let | eq_dual_dual_finTBOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_porderType (T1 : porderType disp1) (T2 : porderType disp2) :
Order.POrder.on (T1 * T2)^d = Order.POrder.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_porderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_bPreorderType (T1 : bPreorderType disp1) (T2 : bPreorderType disp2) :
Order.BPreorder.on (T1 * T2)^d = Order.BPreorder.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_bPreorderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tPreorderType (T1 : tPreorderType disp1) (T2 : tPreorderType disp2) :
Order.TPreorder.on (T1 * T2)^d = Order.TPreorder.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tPreorderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tbPreorderType
(T1 : tbPreorderType disp1) (T2 : tbPreorderType disp2) :
Order.TBPreorder.on (T1 * T2)^d = Order.TBPreorder.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tbPreorderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_bPOrderType (T1 : bPOrderType disp1) (T2 : bPOrderType disp2) :
Order.BPOrder.on (T1 * T2)^d = Order.BPOrder.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_bPOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tPOrderType (T1 : tPOrderType disp1) (T2 : tPOrderType disp2) :
Order.TPOrder.on (T1 * T2)^d = Order.TPOrder.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tPOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tbPOrderType
(T1 : tbPOrderType disp1) (T2 : tbPOrderType disp2) :
Order.TBPOrder.on (T1 * T2)^d = Order.TBPOrder.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tbPOrderType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_meetSemilatticeType
(T1 : meetSemilatticeType disp1) (T2 : meetSemilatticeType disp2) :
Order.MeetSemilattice.on (T1 * T2)^d
= Order.MeetSemilattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_meetSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_bMeetSemilatticeType
(T1 : bMeetSemilatticeType disp1) (T2 : bMeetSemilatticeType disp2) :
Order.BMeetSemilattice.on (T1 * T2)^d
= Order.BMeetSemilattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_bMeetSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tMeetSemilatticeType
(T1 : tMeetSemilatticeType disp1) (T2 : tMeetSemilatticeType disp2) :
Order.TMeetSemilattice.on (T1 * T2)^d
= Order.TMeetSemilattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tMeetSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tbMeetSemilatticeType
(T1 : tbMeetSemilatticeType disp1) (T2 : tbMeetSemilatticeType disp2) :
Order.TBMeetSemilattice.on (T1 * T2)^d
= Order.TBMeetSemilattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tbMeetSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_joinSemilatticeType
(T1 : joinSemilatticeType disp1) (T2 : joinSemilatticeType disp2) :
Order.JoinSemilattice.on (T1 * T2)^d
= Order.JoinSemilattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_joinSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_bJoinSemilatticeType
(T1 : bJoinSemilatticeType disp1) (T2 : bJoinSemilatticeType disp2) :
Order.BJoinSemilattice.on (T1 * T2)^d
= Order.BJoinSemilattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_bJoinSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tJoinSemilatticeType
(T1 : tJoinSemilatticeType disp1) (T2 : tJoinSemilatticeType disp2) :
Order.TJoinSemilattice.on (T1 * T2)^d
= Order.TJoinSemilattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tJoinSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tbJoinSemilatticeType
(T1 : tbJoinSemilatticeType disp1) (T2 : tbJoinSemilatticeType disp2) :
Order.TBJoinSemilattice.on (T1 * T2)^d
= Order.TBJoinSemilattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tbJoinSemilatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_latticeType (T1 : latticeType disp1) (T2 : latticeType disp2) :
Order.Lattice.on (T1 * T2)^d = Order.Lattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_latticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_bLatticeType
(T1 : bLatticeType disp1) (T2 : bLatticeType disp2) :
Order.BLattice.on (T1 * T2)^d = Order.BLattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_bLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tLatticeType
(T1 : tLatticeType disp1) (T2 : tLatticeType disp2) :
Order.TLattice.on (T1 * T2)^d = Order.TLattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tbLatticeType
(T1 : tbLatticeType disp1) (T2 : tbLatticeType disp2) :
Order.TBLattice.on (T1 * T2)^d
= Order.TBLattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tbLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_distrLatticeType
(T1 : distrLatticeType disp1) (T2 : distrLatticeType disp2) :
Order.DistrLattice.on (T1 * T2)^d
= Order.DistrLattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_distrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_bDistrLatticeType
(T1 : bDistrLatticeType disp1) (T2 : bDistrLatticeType disp2) :
Order.BDistrLattice.on (T1 * T2)^d
= Order.BDistrLattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_bDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tDistrLatticeType
(T1 : tDistrLatticeType disp1) (T2 : tDistrLatticeType disp2) :
Order.TDistrLattice.on (T1 * T2)^d
= Order.TDistrLattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_tbDistrLatticeType
(T1 : tbDistrLatticeType disp1) (T2 : tbDistrLatticeType disp2) :
Order.TBDistrLattice.on (T1 * T2)^d
= Order.TBDistrLattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_tbDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_cDistrLatticeType
(T1 : cDistrLatticeType disp1) (T2 : cDistrLatticeType disp2) :
Order.CDistrLattice.on (T1 * T2)^d
= Order.CDistrLattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_cDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_cbDistrLatticeType
(T1 : cbDistrLatticeType disp1) (T2 : cbDistrLatticeType disp2) :
Order.CBDistrLattice.on (T1 * T2)^d
= Order.CBDistrLattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_cbDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_ctDistrLatticeType
(T1 : ctDistrLatticeType disp1) (T2 : ctDistrLatticeType disp2) :
Order.CTDistrLattice.on (T1 * T2)^d
= Order.CTDistrLattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_ctDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_dual_prod_ctbDistrLatticeType
(T1 : ctbDistrLatticeType disp1) (T2 : ctbDistrLatticeType disp2) :
Order.CTBDistrLattice.on (T1 * T2)^d
= Order.CTBDistrLattice.on (T1^d * T2^d)%type | := erefl. | Let | eq_dual_prod_ctbDistrLatticeType | test_suite | test_suite/test_order_conv.v | [
"mathcomp",
"boot",
"order",
"Order.Theory",
"DefaultProdOrder"
] | [
"on",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_vars :
q * w * e * r * t * y * u * i * o * p * a * s * d * f * g * h * j * k * l =
l * w * e * r * t * y * u * i * o * p * a * s * d * f * g * h * j * k * q. | Proof. ring. Qed. | Lemma | test_vars | test_suite | test_suite/test_ring.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"ring_tactic",
"GRing.Theory"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
f1 | :=
x1^3*x2 - x1*x2^3 - x1^3*x3 + x2^3*x3 + x1*x3^3 - x2*x3^3 - x2*y1^
2 + x3*y1^2 + x1*y2^2 - x3*y2^2 - x1*y3^2 + x2*y3^2. | Definition | f1 | test_suite | test_suite/test_ring_from_sander.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"ring_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
f2 | := 2*x1^6*x2^3 -
6*x1^4*x2^5 + 6*x1^2*x2^7 - 2*x2^9 - 6*x1^6*x2^ 2*x3 +
6*x1^5*x2^3*x3 + 12*x1^4*x2^4*x3 - 12*x1^3*x2^5*x3 -
6*x1^2*x2^6*x3 + 6*x1*x2^7*x3 + 6*x1^6*x2*x3^2 -
18*x1^5*x2^2*x3^2 + 6*x1^4*x2^3*x3^2 + 24*x1^3*x2^4*x3^2 -
18*x1^2*x2^5*x3^2 - 6*x1*x2^6*x3^2 + 6*x2^7*x3^2 - 2*x1^6*x3^3
+ 18*x1^5*x2... | Definition | f2 | test_suite | test_suite/test_ring_from_sander.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"ring_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
f3 | := 2*x1^9*x2^4 -
8*x1^7*x2^6 + 12*x1^5*x2^8 - 8*x1^3*x2^10 + 2*x1*x2^12 -
8*x1^9*x2^3*x3 + 6*x1^ 8*x2^4*x3 + 24*x1^7*x2^5*x3 -
16*x1^6*x2^6*x3 - 24*x1^5*x2^7*x3 + 12*x1^4*x2^ 8*x3 +
8*x1^3*x2^9*x3 - 2*x2^12*x3 + 12*x1^9*x2^2*x3^2 -
24*x1^ 8*x2^3*x3^2 - 12*x1^7*x2^4*x3^2 + 48*x1^6*x2^5*x3^2 -
12*x1^5*x2^6*x3^2 - 24*... | Definition | f3 | test_suite | test_suite/test_ring_from_sander.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"ring_tactic"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
from_sander_int (x1 x2 x3 y1 y2 y3 : int) :
f1 x1 x2 x3 y1 y2 y3 * f2 x1 x2 x3 y1 y2 y3 = f3 x1 x2 x3 y1 y2 y3. | Proof.
rewrite /f1 /f2 /f3.
Time ring. (* 6.881 secs *)
Time Qed. | Lemma | from_sander_int | test_suite | test_suite/test_ring_from_sander.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"ring_tactic"
] | [
"f1",
"f2",
"f3",
"int"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
from_sander_rat (x1 x2 x3 y1 y2 y3 : rat) :
f1 x1 x2 x3 y1 y2 y3 * f2 x1 x2 x3 y1 y2 y3 = f3 x1 x2 x3 y1 y2 y3. | Proof.
rewrite /f1 /f2 /f3.
Time ring. (* 6.805 secs *)
Time Qed. | Lemma | from_sander_rat | test_suite | test_suite/test_ring_from_sander.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"ring_tactic"
] | [
"f1",
"f2",
"f3",
"rat"
] | 0.95 secs | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
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