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
value |
|---|---|---|---|---|---|---|---|---|---|---|
mulrzBl_nat (m n : nat) x : x *~ (m%:Z - n%:Z) = x *~ m - x *~ n. | Proof.
wlog/subnK <-: m n / (n <= m)%N; last by rewrite -!pmulrn PoszD mulrnDr !addrK.
have [hmn|/ltnW hmn] := leqP n m; first exact.
by rewrite -[in LHS]opprB -[RHS]opprB subzn // -nmulrn pmulrn -subzn // => ->.
Qed. | Lemma | mulrzBl_nat | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"PoszD",
"addrK",
"last",
"leqP",
"ltnW",
"mulrnDr",
"nat",
"nmulrn",
"opprB",
"pmulrn",
"subnK",
"subzn"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrzDr x : {morph *~%R x : m n / m + n}. | Proof.
by case=> []m []n; rewrite ?NegzE /intmul /= -/(intmul _ _) -?opprD;
rewrite -?[- _ + _]addrC ?mulrzBl_nat // -mulrnDr // addnS.
Qed. | Fact | mulrzDr | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"NegzE",
"addnS",
"addrC",
"intmul",
"mulrnDr",
"mulrzBl_nat",
"opprD"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scalezrE n x : n *: (x : M^z) = x *~ n. | Proof. by []. Qed. | Lemma | scalezrE | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrzA x m n : x *~ (m * n) = x *~ m *~ n. | Proof. by rewrite -!scalezrE scalerA mulrC. Qed. | Lemma | mulrzA | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrC",
"scalerA",
"scalezrE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulr0z x : x *~ 0 = 0. | Proof. by []. Qed. | Lemma | mulr0z | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mul0rz n : 0 *~ n = 0 :> M. | Proof. by rewrite -scalezrE scaler0. Qed. | Lemma | mul0rz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"scaler0",
"scalezrE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrNz x n : x *~ (- n) = - (x *~ n). | Proof. by rewrite -scalezrE scaleNr. Qed. | Lemma | mulrNz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"scaleNr",
"scalezrE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrN1z x : x *~ (- 1) = - x. | Proof. by rewrite -scalezrE scaleN1r. Qed. | Lemma | mulrN1z | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"scaleN1r",
"scalezrE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulNrz x n : (- x) *~ n = - (x *~ n). | Proof. by rewrite -scalezrE scalerN. Qed. | Lemma | mulNrz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"scalerN",
"scalezrE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrzBr x m n : x *~ (m - n) = x *~ m - x *~ n. | Proof. by rewrite -scalezrE scalerBl. Qed. | Lemma | mulrzBr | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"scalerBl",
"scalezrE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrzBl x y n : (x - y) *~ n = x *~ n - y *~ n. | Proof. by rewrite -scalezrE scalerBr. Qed. | Lemma | mulrzBl | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"scalerBr",
"scalezrE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrz_nat (n : nat) x : x *~ n%:R = x *+ n. | Proof. by rewrite -scalezrE scaler_nat. Qed. | Lemma | mulrz_nat | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"nat",
"scaler_nat",
"scalezrE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrz_sumr : forall x I r (P : pred I) F,
x *~ (\sum_(i <- r | P i) F i) = \sum_(i <- r | P i) x *~ F i. | Proof. by rewrite -/M^z; apply: scaler_suml. Qed. | Lemma | mulrz_sumr | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"apply",
"scaler_suml"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrz_suml : forall n I r (P : pred I) (F : I -> M),
(\sum_(i <- r | P i) F i) *~ n= \sum_(i <- r | P i) F i *~ n. | Proof. by rewrite -/M^z; apply: scaler_sumr. Qed. | Lemma | mulrz_suml | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"apply",
"scaler_sumr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrzDl_tmp | := mulrzDl. | Notation | mulrzDl_tmp | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzDl"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrzDr_tmp | := mulrzDr. | Notation | mulrzDr_tmp | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzDr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ffunMzE (I : finType) (M : zmodType) (f : {ffun I -> M}) z x :
(f *~ z) x = f x *~ z. | Proof. by case: z => n; rewrite ?ffunE ffunMnE. Qed. | Lemma | ffunMzE | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ffunE",
"ffunMnE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
intz (n : int) : n%:~R = n. | Proof. by case: n => n; rewrite ?NegzE /intmul/= -(rmorphMn Posz)/= natn. Qed. | Lemma | intz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"NegzE",
"Posz",
"int",
"intmul",
"natn",
"rmorphMn"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
natz (n : nat) : n%:R = n%:Z :> int. | Proof. by rewrite pmulrn intz. Qed. | Lemma | natz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"int",
"intz",
"nat",
"pmulrn"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrzAl n x y : (x *~ n) * y = (x * y) *~ n. | Proof. by case: n => n; rewrite ?mulNr mulrnAl. Qed. | Lemma | mulrzAl | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulNr",
"mulrnAl"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrzAr n x y : x * (y *~ n) = (x * y) *~ n. | Proof. by case: n => n; rewrite ?mulrN mulrnAr. Qed. | Lemma | mulrzAr | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrN",
"mulrnAr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrzl x n : n%:~R * x = x *~ n. | Proof. by rewrite mulrzAl mul1r. Qed. | Lemma | mulrzl | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mul1r",
"mulrzAl"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrzr x n : x * n%:~R = x *~ n. | Proof. by rewrite mulrzAr mulr1. Qed. | Lemma | mulrzr | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulr1",
"mulrzAr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulNrNz n x : (- x) *~ (- n) = x *~ n. | Proof. by rewrite mulNrz mulrNz opprK. Qed. | Lemma | mulNrNz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulNrz",
"mulrNz",
"opprK"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrbz x (b : bool) : x *~ b = (if b then x else 0). | Proof. by case: b. Qed. | Lemma | mulrbz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
intrN n : (- n)%:~R = - n%:~R :> R. | Proof. exact: mulrNz. Qed. | Lemma | intrN | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrNz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
intrD m n : (m + n)%:~R = m%:~R + n%:~R :> R. | Proof. exact: mulrzDr. Qed. | Lemma | intrD | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzDr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
intrD1 m : (m + 1)%:~R = m%:~R + 1 :> R. | Proof. by rewrite intrD. Qed. | Lemma | intrD1 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"intrD"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
intr1D m : (1 + m)%:~R = 1 + m%:~R :> R. | Proof. by rewrite intrD. Qed. | Lemma | intr1D | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"intrD"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
intrB m n : (m - n)%:~R = m%:~R - n%:~R :> R. | Proof. exact: mulrzBr. Qed. | Lemma | intrB | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzBr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
intrM m n : (m * n)%:~R = m%:~R * n%:~R :> R. | Proof. by rewrite mulrzA -mulrzr. Qed. | Lemma | intrM | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzA",
"mulrzr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
intmul1_is_monoid_morphism : monoid_morphism ( *~%R (1 : R)). | Proof. by split; move=> // x y /=; rewrite intrM. Qed. | Lemma | intmul1_is_monoid_morphism | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"intrM",
"monoid_morphism",
"split"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
intmul1_is_multiplicative | :=
(fun g => (g.2,g.1)) intmul1_is_monoid_morphism. | Definition | intmul1_is_multiplicative | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"intmul1_is_monoid_morphism"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulr2z n : n *~ 2 = n + n. | Proof. exact: mulr2n. Qed. | Lemma | mulr2z | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
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"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulr2n"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrzz m n : m *~ n = m * n. | Proof. by rewrite -mulrzr intz. Qed. | Lemma | mulrzz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
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"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"intz",
"mulrzr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulz2 n : n * 2%:Z = n + n. | Proof. by rewrite -mulrzz. Qed. | Lemma | mulz2 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"bigop",
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"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mul2z n : 2%:Z * n = n + n. | Proof. by rewrite mulrC -mulrzz. Qed. | Lemma | mul2z | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"finfun",
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"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrC",
"mulrzz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scaler_int n v : n%:~R *: v = v *~ n. | Proof. by case: n => n; rewrite /intmul ?scaleNr scaler_nat. Qed. | Lemma | scaler_int | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
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"finfun",
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"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"intmul",
"scaleNr",
"scaler_nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scalerMzl a v n : (a *: v) *~ n = (a *~ n) *: v. | Proof. by rewrite -mulrzl -scaler_int scalerA. Qed. | Lemma | scalerMzl | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzl",
"scalerA",
"scaler_int"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scalerMzr a v n : (a *: v) *~ n = a *: (v *~ n). | Proof. by rewrite -!scaler_int !scalerA mulrzr mulrzl. Qed. | Lemma | scalerMzr | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
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"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzl",
"mulrzr",
"scalerA",
"scaler_int"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrz_int (M : zmodType) (n : int) (x : M) : x *~ n%:~R = x *~ n. | Proof. by rewrite -scalezrE scaler_int. Qed. | Lemma | mulrz_int | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"int",
"scaler_int",
"scalezrE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
raddfMz n : {morph f : x / x *~ n}. | Proof. by case: n=> n x; rewrite 1?raddfN raddfMn. Qed. | Lemma | raddfMz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"raddfMn",
"raddfN"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rmorphMz : forall n, {morph f : x / x *~ n}. | Proof. exact: raddfMz. Qed. | Lemma | rmorphMz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"raddfMz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rmorph_int : forall n, f n%:~R = n%:~R. | Proof. by move=> n; rewrite rmorphMz rmorph1. Qed. | Lemma | rmorph_int | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"rmorph1",
"rmorphMz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
linearMn : forall n, {morph f : x / x *~ n}. | Proof. exact: raddfMz. Qed. | Lemma | linearMn | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
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"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"raddfMz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
raddf_int_scalable (aV rV : lmodType int) (f : {additive aV -> rV}) :
scalable f. | Proof. by move=> z u; rewrite -[z]intz !scaler_int raddfMz. Qed. | Lemma | raddf_int_scalable | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"additive",
"int",
"intz",
"raddfMz",
"scalable",
"scaler_int"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
commrMz (x y : R) n : GRing.comm x y -> GRing.comm x (y *~ n). | Proof. by rewrite /GRing.comm=> com_xy; rewrite mulrzAr mulrzAl com_xy. Qed. | Lemma | commrMz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"comm",
"mulrzAl",
"mulrzAr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
commr_int (x : R) n : GRing.comm x n%:~R. | Proof. exact/commrMz/commr1. Qed. | Lemma | commr_int | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
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"finfun",
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"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"comm",
"commr1",
"commrMz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
sumMz : forall I r (P : pred I) F,
(\sum_(i <- r | P i) F i)%N%:~R = \sum_(i <- r | P i) ((F i)%:~R) :> R. | Proof. exact: rmorph_sum. Qed. | Lemma | sumMz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"rmorph_sum"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
prodMz : forall I r (P : pred I) F,
(\prod_(i <- r | P i) F i)%N%:~R = \prod_(i <- r | P i) ((F i)%:~R) :> R. | Proof. exact: rmorph_prod. Qed. | Lemma | prodMz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"rmorph_prod"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pcharFp : p \in [pchar R]. | Hypothesis | pcharFp | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
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"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | ||
"x ^f" | := (pFrobenius_aut pcharFp x). | Notation | x ^f | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"pFrobenius_aut",
"pcharFp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pFrobenius_autMz x n : (x *~ n)^f = x^f *~ n. | Proof.
case: n=> n /=; first exact: pFrobenius_autMn.
by rewrite !NegzE !mulrNz pFrobenius_autN pFrobenius_autMn.
Qed. | Lemma | pFrobenius_autMz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"NegzE",
"mulrNz",
"pFrobenius_autMn",
"pFrobenius_autN"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pFrobenius_aut_int n : (n%:~R)^f = n%:~R. | Proof. by rewrite pFrobenius_autMz pFrobenius_aut1. Qed. | Lemma | pFrobenius_aut_int | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"pFrobenius_aut1",
"pFrobenius_autMz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autMz | := (pFrobenius_autMz) (only parsing). | Notation | Frobenius_autMz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"pFrobenius_autMz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_aut_int | := (pFrobenius_aut_int) (only parsing). | Notation | Frobenius_aut_int | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"pFrobenius_aut_int"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rmorphzP (f : {rmorphism int -> R}) : f =1 ( *~%R 1). | Proof. by move=> n; rewrite -[n in LHS]intz rmorph_int. Qed. | Lemma | rmorphzP | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"int",
"intz",
"rmorph_int"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ler_pMz2r n (hn : 0 < n) : {mono *~%R^~ n :x y / x <= y :> R}. | Proof. by move=> x y; case: n hn=> [[]|] // n _; rewrite ler_pMn2r. Qed. | Lemma | ler_pMz2r | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_pMn2r"
] | intmul and ler/ltr | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
ltr_pMz2r n (hn : 0 < n) : {mono *~%R^~ n : x y / x < y :> R}. | Proof. exact: leW_mono (ler_pMz2r _). Qed. | Lemma | ltr_pMz2r | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
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"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"leW_mono",
"ler_pMz2r"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ler_nMz2r n (hn : n < 0) : {mono *~%R^~ n : x y /~ x <= y :> R}. | Proof.
by move=> x y /=; rewrite -![_ *~ n]mulNrNz ler_pMz2r (oppr_cp0, lerN2).
Qed. | Lemma | ler_nMz2r | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"lerN2",
"ler_pMz2r",
"mulNrNz",
"oppr_cp0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltr_nMz2r n (hn : n < 0) : {mono *~%R^~ n : x y /~ x < y :> R}. | Proof. exact: leW_nmono (ler_nMz2r _). Qed. | Lemma | ltr_nMz2r | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"leW_nmono",
"ler_nMz2r"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ler_wpMz2r n (hn : 0 <= n) : {homo *~%R^~ n : x y / x <= y :> R}. | Proof. by move=> x y xy; case: n hn=> [] // n _; rewrite ler_wMn2r. Qed. | Lemma | ler_wpMz2r | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
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"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_wMn2r"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ler_wnMz2r n (hn : n <= 0) : {homo *~%R^~ n : x y /~ x <= y :> R}. | Proof. by move=> x y xy /=; rewrite -lerN2 -!mulrNz ler_wpMz2r // oppr_ge0. Qed. | Lemma | ler_wnMz2r | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
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"nmodule",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"lerN2",
"ler_wpMz2r",
"mulrNz",
"oppr_ge0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrz_ge0 x n (x0 : 0 <= x) (n0 : 0 <= n) : 0 <= x *~ n. | Proof. by rewrite -(mul0rz _ n) ler_wpMz2r. Qed. | Lemma | mulrz_ge0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_wpMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrz_le0 x n (x0 : x <= 0) (n0 : n <= 0) : 0 <= x *~ n. | Proof. by rewrite -(mul0rz _ n) ler_wnMz2r. Qed. | Lemma | mulrz_le0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_wnMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrz_ge0_le0 x n (x0 : 0 <= x) (n0 : n <= 0) : x *~ n <= 0. | Proof. by rewrite -(mul0rz _ n) ler_wnMz2r. Qed. | Lemma | mulrz_ge0_le0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_wnMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrz_le0_ge0 x n (x0 : x <= 0) (n0 : 0 <= n) : x *~ n <= 0. | Proof. by rewrite -(mul0rz _ n) ler_wpMz2r. Qed. | Lemma | mulrz_le0_ge0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_wpMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pmulrz_lgt0 x n (n0 : 0 < n) : (0 < x *~ n) = (0 < x). | Proof. by rewrite -(mul0rz _ n) ltr_pMz2r // mul0rz. Qed. | Lemma | pmulrz_lgt0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
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"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ltr_pMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nmulrz_lgt0 x n (n0 : n < 0) : (0 < x *~ n) = (x < 0). | Proof. by rewrite -(mul0rz _ n) ltr_nMz2r // mul0rz. Qed. | Lemma | nmulrz_lgt0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ltr_nMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pmulrz_llt0 x n (n0 : 0 < n) : (x *~ n < 0) = (x < 0). | Proof. by rewrite -(mul0rz _ n) ltr_pMz2r // mul0rz. Qed. | Lemma | pmulrz_llt0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ltr_pMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nmulrz_llt0 x n (n0 : n < 0) : (x *~ n < 0) = (0 < x). | Proof. by rewrite -(mul0rz _ n) ltr_nMz2r // mul0rz. Qed. | Lemma | nmulrz_llt0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ltr_nMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pmulrz_lge0 x n (n0 : 0 < n) : (0 <= x *~ n) = (0 <= x). | Proof. by rewrite -(mul0rz _ n) ler_pMz2r // mul0rz. Qed. | Lemma | pmulrz_lge0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_pMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nmulrz_lge0 x n (n0 : n < 0) : (0 <= x *~ n) = (x <= 0). | Proof. by rewrite -(mul0rz _ n) ler_nMz2r // mul0rz. Qed. | Lemma | nmulrz_lge0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_nMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pmulrz_lle0 x n (n0 : 0 < n) : (x *~ n <= 0) = (x <= 0). | Proof. by rewrite -(mul0rz _ n) ler_pMz2r // mul0rz. Qed. | Lemma | pmulrz_lle0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_pMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nmulrz_lle0 x n (n0 : n < 0) : (x *~ n <= 0) = (0 <= x). | Proof. by rewrite -(mul0rz _ n) ler_nMz2r // mul0rz. Qed. | Lemma | nmulrz_lle0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_nMz2r",
"mul0rz"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ler_wpMz2l x (hx : 0 <= x) : {homo *~%R x : x y / x <= y}. | Proof.
by move=> m n /= hmn; rewrite -subr_ge0 -mulrzBr mulrz_ge0 // subr_ge0.
Qed. | Lemma | ler_wpMz2l | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
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"divalg",
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"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzBr",
"mulrz_ge0",
"subr_ge0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ler_wnMz2l x (hx : x <= 0) : {homo *~%R x : x y /~ x <= y}. | Proof.
by move=> m n /= hmn; rewrite -subr_ge0 -mulrzBr mulrz_le0 // subr_le0.
Qed. | Lemma | ler_wnMz2l | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
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"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzBr",
"mulrz_le0",
"subr_ge0",
"subr_le0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ler_pMz2l x (hx : 0 < x) : {mono *~%R x : x y / x <= y}. | Proof.
move=> m n /=; rewrite real_mono ?num_real // => {m n}.
by move=> m n /= hmn; rewrite -subr_gt0 -mulrzBr pmulrz_lgt0 // subr_gt0.
Qed. | Lemma | ler_pMz2l | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
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"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzBr",
"num_real",
"pmulrz_lgt0",
"real_mono",
"subr_gt0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ler_nMz2l x (hx : x < 0) : {mono *~%R x : x y /~ x <= y}. | Proof.
move=> m n /=; rewrite real_nmono ?num_real // => {m n}.
by move=> m n /= hmn; rewrite -subr_gt0 -mulrzBr nmulrz_lgt0 // subr_lt0.
Qed. | Lemma | ler_nMz2l | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
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"bigop",
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"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"mulrzBr",
"nmulrz_lgt0",
"num_real",
"real_nmono",
"subr_gt0",
"subr_lt0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltr_pMz2l x (hx : 0 < x) : {mono *~%R x : x y / x < y}. | Proof. exact: leW_mono (ler_pMz2l _). Qed. | Lemma | ltr_pMz2l | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
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"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"leW_mono",
"ler_pMz2l"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltr_nMz2l x (hx : x < 0) : {mono *~%R x : x y /~ x < y}. | Proof. exact: leW_nmono (ler_nMz2l _). Qed. | Lemma | ltr_nMz2l | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"leW_nmono",
"ler_nMz2l"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pmulrz_rgt0 x n (x0 : 0 < x) : (0 < x *~ n) = (0 < n). | Proof. by rewrite -(mulr0z x) ltr_pMz2l. Qed. | Lemma | pmulrz_rgt0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"divalg",
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"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ltr_pMz2l",
"mulr0z"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nmulrz_rgt0 x n (x0 : x < 0) : (0 < x *~ n) = (n < 0). | Proof. by rewrite -(mulr0z x) ltr_nMz2l. Qed. | Lemma | nmulrz_rgt0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ltr_nMz2l",
"mulr0z"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pmulrz_rlt0 x n (x0 : 0 < x) : (x *~ n < 0) = (n < 0). | Proof. by rewrite -(mulr0z x) ltr_pMz2l. Qed. | Lemma | pmulrz_rlt0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
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"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ltr_pMz2l",
"mulr0z"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nmulrz_rlt0 x n (x0 : x < 0) : (x *~ n < 0) = (0 < n). | Proof. by rewrite -(mulr0z x) ltr_nMz2l. Qed. | Lemma | nmulrz_rlt0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ltr_nMz2l",
"mulr0z"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pmulrz_rge0 x n (x0 : 0 < x) : (0 <= x *~ n) = (0 <= n). | Proof. by rewrite -(mulr0z x) ler_pMz2l. Qed. | Lemma | pmulrz_rge0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_pMz2l",
"mulr0z"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nmulrz_rge0 x n (x0 : x < 0) : (0 <= x *~ n) = (n <= 0). | Proof. by rewrite -(mulr0z x) ler_nMz2l. Qed. | Lemma | nmulrz_rge0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_nMz2l",
"mulr0z"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pmulrz_rle0 x n (x0 : 0 < x) : (x *~ n <= 0) = (n <= 0). | Proof. by rewrite -(mulr0z x) ler_pMz2l. Qed. | Lemma | pmulrz_rle0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_pMz2l",
"mulr0z"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nmulrz_rle0 x n (x0 : x < 0) : (x *~ n <= 0) = (0 <= n). | Proof. by rewrite -(mulr0z x) ler_nMz2l. Qed. | Lemma | nmulrz_rle0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_nMz2l",
"mulr0z"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrIz x (hx : x != 0) : injective ( *~%R x). | Proof.
move=> y z; rewrite -![x *~ _]mulrzr => /(mulfI hx).
by apply: inc_inj y z; exact: ler_pMz2l.
Qed. | Lemma | mulrIz | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"apply",
"inc_inj",
"ler_pMz2l",
"mulfI",
"mulrzr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ler_int m n : (m%:~R <= n%:~R :> R) = (m <= n). | Proof. by rewrite ler_pMz2l. Qed. | Lemma | ler_int | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_pMz2l"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltr_int m n : (m%:~R < n%:~R :> R) = (m < n). | Proof. by rewrite ltr_pMz2l. Qed. | Lemma | ltr_int | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ltr_pMz2l"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eqr_int m n : (m%:~R == n%:~R :> R) = (m == n). | Proof. by rewrite (inj_eq (mulrIz _)) ?oner_eq0. Qed. | Lemma | eqr_int | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"inj_eq",
"mulrIz",
"oner_eq0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ler0z n : (0 <= n%:~R :> R) = (0 <= n). | Proof. by rewrite pmulrz_rge0. Qed. | Lemma | ler0z | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"pmulrz_rge0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltr0z n : (0 < n%:~R :> R) = (0 < n). | Proof. by rewrite pmulrz_rgt0. Qed. | Lemma | ltr0z | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"pmulrz_rgt0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lerz0 n : (n%:~R <= 0 :> R) = (n <= 0). | Proof. by rewrite pmulrz_rle0. Qed. | Lemma | lerz0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"pmulrz_rle0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltrz0 n : (n%:~R < 0 :> R) = (n < 0). | Proof. by rewrite pmulrz_rlt0. Qed. | Lemma | ltrz0 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"pmulrz_rlt0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ler1z (n : int) : (1 <= n%:~R :> R) = (1 <= n). | Proof. by rewrite -[1]/(1%:~R) ler_int. Qed. | Lemma | ler1z | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"int",
"ler_int"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltr1z (n : int) : (1 < n%:~R :> R) = (1 < n). | Proof. by rewrite -[1]/(1%:~R) ltr_int. Qed. | Lemma | ltr1z | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"int",
"ltr_int"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lerz1 n : (n%:~R <= 1 :> R) = (n <= 1). | Proof. by rewrite -[1]/(1%:~R) ler_int. Qed. | Lemma | lerz1 | algebra | algebra/ssrint.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"fintype",
"finfun",
"bigop",
"order",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"countalg",
"poly",
"orderedzmod",
"numdomain",
"numfield",
"Order.TTheory",
... | [
"ler_int"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
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