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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|---|---|---|---|---|---|---|---|---|---|---|
from_sander_abstract (R : comUnitRingType) (x1 x2 x3 y1 y2 y3 : R) :
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. (* 6.303 secs *)
Time Qed. | Lemma | from_sander_abstract | test_suite | test_suite/test_ring_from_sander.v | [
"mathcomp",
"all_boot",
"ssralg",
"ssrnum",
"ssrint",
"rat",
"ring_tactic"
] | [
"f1",
"f2",
"f3"
] | 0.94 secs | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). | Proof. time by rewrite orbACA. Abort. | Lemma | test_orb | test_suite | test_suite/test_ssrAC.v | [
"mathcomp",
"boot",
"ssralg",
"GRing.Theory"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). | Proof. time by rewrite (AC (2*2) ((1*3)*(2*4))). Abort. | Lemma | test_orb | test_suite | test_suite/test_ssrAC.v | [
"mathcomp",
"boot",
"ssralg",
"GRing.Theory"
] | [
"AC"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_orb (a b c d : bool) : (a || b) || (c || d) = (a || c) || (b || d). | Proof. time by rewrite orb.[AC (2*2) ((1*3)*(2*4))]. Qed. | Lemma | test_orb | test_suite | test_suite/test_ssrAC.v | [
"mathcomp",
"boot",
"ssralg",
"GRing.Theory"
] | [
"AC"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_addn (a b c d : nat) : a + b + c + d = a + c + b + d. | Proof. time by rewrite -addnA addnAC addnA addnAC. Abort. | Lemma | test_addn | test_suite | test_suite/test_ssrAC.v | [
"mathcomp",
"boot",
"ssralg",
"GRing.Theory"
] | [
"addnA",
"addnAC",
"nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_addn (a b c d : nat) : a + b + c + d = a + c + b + d. | Proof. time by rewrite (ACl (1*3*2*4)). Abort. | Lemma | test_addn | test_suite | test_suite/test_ssrAC.v | [
"mathcomp",
"boot",
"ssralg",
"GRing.Theory"
] | [
"ACl",
"nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_addn (a b c d : nat) : a + b + c + d = a + c + b + d. | Proof. time by rewrite addn.[ACl 1*3*2*4]. Qed. | Lemma | test_addn | test_suite | test_suite/test_ssrAC.v | [
"mathcomp",
"boot",
"ssralg",
"GRing.Theory"
] | [
"ACl",
"addn",
"nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_addr (R : comRingType) (a b c d : R) : (a + b + c + d = a + c + b + d)%R. | Proof. time by rewrite -GRing.addrA GRing.addrAC GRing.addrA GRing.addrAC. Abort. | Lemma | test_addr | test_suite | test_suite/test_ssrAC.v | [
"mathcomp",
"boot",
"ssralg",
"GRing.Theory"
] | [
"addrA",
"addrAC",
"comRingType"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_addr (R : comRingType) (a b c d : R) : (a + b + c + d = a + c + b + d)%R. | Proof. time by rewrite (ACl (1*3*2*4)). Abort. | Lemma | test_addr | test_suite | test_suite/test_ssrAC.v | [
"mathcomp",
"boot",
"ssralg",
"GRing.Theory"
] | [
"ACl",
"comRingType"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_addr (R : comRingType) (a b c d : R) : (a + b + c + d = a + c + b + d)%R. | Proof. time by rewrite (@GRing.add R).[ACl 1*3*2*4]. Qed. | Lemma | test_addr | test_suite | test_suite/test_ssrAC.v | [
"mathcomp",
"boot",
"ssralg",
"GRing.Theory"
] | [
"ACl",
"add",
"comRingType"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
test_mulr (R : comRingType) (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : R)
(x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 : R) :
(x0 * x1) * (x2 * x3) * (x4 * x5) * (x6 * x7 * x8 * x9) *
(x10 * x11) * (x12 * x13) * (x14 * x15) * (x16 * x17 * x18 * x19) *
(x0 * x1) * (x2 * x3) * (x4 * x5) * (x6 * x7 * x8 * x9) *
(x10 * ... | Proof.
pose s := ((2 * 4 * 9 * 1 * 3 * 5 * 7 * 6 * 8 * 20 * 21 * 22 * 23) * 25 * 26 * 27 * 28
* (29 * 30 * 31) * 32 * 33 * 34 * 35 * 36 * 37 * 38 * 39 * 40 * 41
* (10 * 12 * 14 * 19 * 11 * 13 * 15 * 17 * 16 * 18 * 24)
* (42 * 43 * 44 * 45 * 46 * 47 * 48 * 49) * 50
... | Lemma | test_mulr | test_suite | test_suite/test_ssrAC.v | [
"mathcomp",
"boot",
"ssralg",
"GRing.Theory"
] | [
"AC",
"ACl",
"comRingType",
"mul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
B | := mkB x & x \in S. | Inductive | B | test_suite | test_suite/test_subtype_factories.v | [
"HB",
"structures",
"mathcomp",
"boot",
"ssralg"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
vB u | := let: mkB x _ := u in x. | Definition | vB | test_suite | test_suite/test_subtype_factories.v | [
"HB",
"structures",
"mathcomp",
"boot",
"ssralg"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
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