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valM1 : monoid_morphism val.
Proof. exact: valM_subproof. Qed.
Lemma
valM1
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "monoid_morphism", "val" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
oneU : U
:= inU (@rpred1 _ (MulClosed.clone R S _)).
Let
oneU
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "clone", "inU", "rpred1" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulU (u1 u2 : U)
:= inU (rpredM _ _ (valP u1) (valP u2)).
Let
mulU
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "inU", "rpredM", "valP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulrA : associative mulU.
Proof. by move=> x y z; apply: val_inj; rewrite !SubK mulrA. Qed.
Lemma
mulrA
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "mulU", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mul1r : left_id oneU mulU.
Proof. by move=> x; apply: val_inj; rewrite !SubK mul1r. Qed.
Lemma
mul1r
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "mulU", "oneU", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulr1 : right_id oneU mulU.
Proof. by move=> x; apply: val_inj; rewrite !SubK mulr1. Qed.
Lemma
mulr1
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "mulU", "oneU", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulrDl : left_distributive mulU +%R.
Proof. by move=> x y z; apply: val_inj; rewrite !(SubK, raddfD)/= !SubK mulrDl. Qed.
Lemma
mulrDl
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "mulU", "raddfD", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulrDr : right_distributive mulU +%R.
Proof. by move=> x y z; apply: val_inj; rewrite !(SubK, raddfD)/= !SubK mulrDr. Qed.
Lemma
mulrDr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "mulU", "raddfD", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mul0r : left_zero 0%R mulU.
Proof. by move=> x; apply: val_inj; rewrite SubK val0 mul0r. Qed.
Lemma
mul0r
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "mulU", "val0", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulr0 : right_zero 0%R mulU.
Proof. by move=> x; apply: val_inj; rewrite SubK val0 mulr0. Qed.
Lemma
mulr0
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "mulU", "val0", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
valM : monoid_morphism (val : U -> R).
Proof. by split=> [|x y] /=; rewrite !SubK. Qed.
Lemma
valM
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "monoid_morphism", "split", "val" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
oner_neq0 : (1 : U) != 0.
Proof. by rewrite -(inj_eq val_inj) rmorph0 rmorph1 oner_neq0. Qed.
Lemma
oner_neq0
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "inj_eq", "rmorph0", "rmorph1", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulrC : @commutative U U *%R.
Proof. by move=> x y; apply: val_inj; rewrite !rmorphM mulrC. Qed.
Lemma
mulrC
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "apply", "rmorphM", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
val
:= (val : W -> V).
Notation
val
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
inW v Sv : W
:= Sub v Sv.
Let
inW
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Sub", "Sv" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
scaleW a (w : W)
:= inW (rpredZ a _ (valP w)).
Let
scaleW
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "inW", "rpredZ", "valP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
scalerA' a b v : scaleW a (scaleW b v) = scaleW (a * b) v.
Proof. by apply: val_inj; rewrite !SubK scalerA. Qed.
Lemma
scalerA'
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "scaleW", "scalerA", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
scale0r v : scaleW 0 v = 0.
Proof. by apply: val_inj; rewrite SubK scale0r raddf0. Qed.
Lemma
scale0r
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "raddf0", "scaleW", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
scale1r : left_id 1 scaleW.
Proof. by move=> x; apply: val_inj; rewrite SubK scale1r. Qed.
Lemma
scale1r
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "scaleW", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
scalerDr : right_distributive scaleW +%R.
Proof. by move=> a u v; apply: val_inj; rewrite SubK !raddfD/= !SubK. Qed.
Lemma
scalerDr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "raddfD", "scaleW", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
scalerDl v : {morph scaleW^~ v : a b / a + b}.
Proof. by move=> a b; apply: val_inj; rewrite raddfD/= !SubK scalerDl. Qed.
Lemma
scalerDl
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "apply", "raddfD", "scaleW", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
valZ : scalable (val : W -> _).
Proof. by move=> k w; rewrite SubK. Qed.
Fact
valZ
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "SubK", "scalable", "val" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
scalerAl (a : R) (u v : W) : a *: (u * v) = a *: u * v.
Proof. by apply: val_inj; rewrite !(linearZ, rmorphM) /= linearZ scalerAl. Qed.
Lemma
scalerAl
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "apply", "linearZ", "rmorphM", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
scalerAr (k : R) (x y : W) : k *: (x * y) = x * (k *: y).
Proof. by apply: val_inj; rewrite !(linearZ, rmorphM)/= linearZ scalerAr. Qed.
Lemma
scalerAr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "apply", "linearZ", "rmorphM", "val_inj" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubNmodule_isSubNzSemiRing' 'of' U 'by' <: ]"
:= (SubNmodule_isSubNzSemiRing.Build _ _ U (@rpred1M _ _)) (format "[ 'SubNmodule_isSubNzSemiRing' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubNmodule_isSubNzSemiRing' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "rpred1M" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubNmodule_isSubPzSemiRing' 'of' U 'by' <: ]"
:= (SubNmodule_isSubPzSemiRing.Build _ _ U (@rpred1M _ _)) (format "[ 'SubNmodule_isSubPzSemiRing' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubNmodule_isSubPzSemiRing' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "rpred1M" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubNzSemiRing' 'of' U 'by' <: ]"
:= (SubChoice_isSubNzSemiRing.Build _ _ U (semiringClosedP _)) (format "[ 'SubChoice_isSubNzSemiRing' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubNzSemiRing' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "semiringClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubSemiRing_isSubComSemiRing' 'of' U 'by' <: ]"
:= (SubSemiRing_isSubComSemiRing.Build _ _ U) (format "[ 'SubSemiRing_isSubComSemiRing' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubSemiRing_isSubComSemiRing' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubComNzSemiRing' 'of' U 'by' <: ]"
:= (SubChoice_isSubComNzSemiRing.Build _ _ U (semiringClosedP _)) (format "[ 'SubChoice_isSubComNzSemiRing' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubComNzSemiRing' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "semiringClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubComPzSemiRing' 'of' U 'by' <: ]"
:= (SubChoice_isSubComPzSemiRing.Build _ _ U (semiringClosedP _)) (format "[ 'SubChoice_isSubComPzSemiRing' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubComPzSemiRing' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "semiringClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubPzSemiRing' 'of' U 'by' <: ]"
:= (SubChoice_isSubPzSemiRing.Build _ _ U (subringClosedP _)) (format "[ 'SubChoice_isSubPzSemiRing' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubPzSemiRing' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subringClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubPzRing' 'of' U 'by' <: ]"
:= (SubChoice_isSubPzRing.Build _ _ U (subringClosedP _)) (format "[ 'SubChoice_isSubPzRing' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubPzRing' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subringClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubNzRing' 'of' U 'by' <: ]"
:= (SubChoice_isSubNzRing.Build _ _ U (subringClosedP _)) (format "[ 'SubChoice_isSubNzRing' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubNzRing' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subringClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubComPzRing' 'of' U 'by' <: ]"
:= (SubChoice_isSubComPzRing.Build _ _ U (subringClosedP _)) (format "[ 'SubChoice_isSubComPzRing' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubComPzRing' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subringClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubComNzRing' 'of' U 'by' <: ]"
:= (SubChoice_isSubComNzRing.Build _ _ U (subringClosedP _)) (format "[ 'SubChoice_isSubComNzRing' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubComNzRing' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subringClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubNmodule_isSubLSemiModule' 'of' U 'by' <: ]"
:= (SubNmodule_isSubLSemiModule.Build _ _ _ U (subsemimodClosedP _)) (format "[ 'SubNmodule_isSubLSemiModule' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubNmodule_isSubLSemiModule' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subsemimodClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubLSemiModule' 'of' U 'by' <: ]"
:= (SubChoice_isSubLSemiModule.Build _ _ _ U (subsemimodClosedP _)) (format "[ 'SubChoice_isSubLSemiModule' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubLSemiModule' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subsemimodClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubLmodule' 'of' U 'by' <: ]"
:= (SubChoice_isSubLmodule.Build _ _ _ U (subsemimodClosedP _)) (format "[ 'SubChoice_isSubLmodule' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubLmodule' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subsemimodClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubSemiRing_SubLSemiModule_isSubLSemiAlgebra' 'of' U 'by' <: ]"
:= (SubSemiRing_SubLSemiModule_isSubLSemiAlgebra.Build _ _ _ U) (format "[ 'SubSemiRing_SubLSemiModule_isSubLSemiAlgebra' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubSemiRing_SubLSemiModule_isSubLSemiAlgebra' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubRing_SubLmodule_isSubLalgebra' 'of' U 'by' <: ]"
:= (SubRing_SubLmodule_isSubLalgebra.Build _ _ _ U) (format "[ 'SubRing_SubLmodule_isSubLalgebra' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubRing_SubLmodule_isSubLalgebra' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubLSemiAlgebra_isSubSemiAlgebra' 'of' U 'by' <: ]"
:= (SubLSemiAlgebra_isSubSemiAlgebra.Build _ _ _ U) (format "[ 'SubLSemiAlgebra_isSubSemiAlgebra' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubLSemiAlgebra_isSubSemiAlgebra' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubPzLSemiAlgebra' 'of' U 'by' <: ]"
:= (SubChoice_isSubPzLSemiAlgebra.Build _ _ _ U (subsemialgClosedP _)) (format "[ 'SubChoice_isSubPzLSemiAlgebra' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubPzLSemiAlgebra' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subsemialgClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubNzLSemiAlgebra' 'of' U 'by' <: ]"
:= (SubChoice_isSubNzLSemiAlgebra.Build _ _ _ U (subsemialgClosedP _)) (format "[ 'SubChoice_isSubNzLSemiAlgebra' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubNzLSemiAlgebra' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subsemialgClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubPzLalgebra' 'of' U 'by' <: ]"
:= (SubChoice_isSubPzLalgebra.Build _ _ _ U (subsemialgClosedP _)) (format "[ 'SubChoice_isSubPzLalgebra' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubPzLalgebra' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subsemialgClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubNzLalgebra' 'of' U 'by' <: ]"
:= (SubChoice_isSubNzLalgebra.Build _ _ _ U (subsemialgClosedP _)) (format "[ 'SubChoice_isSubNzLalgebra' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubNzLalgebra' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subsemialgClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubPzSemiAlgebra' 'of' U 'by' <: ]"
:= (SubChoice_isSubPzSemiAlgebra.Build _ _ _ U (subsemialgClosedP _)) (format "[ 'SubChoice_isSubPzSemiAlgebra' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubPzSemiAlgebra' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subsemialgClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubNzSemiAlgebra' 'of' U 'by' <: ]"
:= (SubChoice_isSubNzSemiAlgebra.Build _ _ _ U (subsemialgClosedP _)) (format "[ 'SubChoice_isSubNzSemiAlgebra' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubNzSemiAlgebra' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subsemialgClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubPzAlgebra' 'of' U 'by' <: ]"
:= (SubChoice_isSubPzAlgebra.Build _ _ _ U (subsemialgClosedP _)) (format "[ 'SubChoice_isSubPzAlgebra' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubPzAlgebra' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subsemialgClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
"[ 'SubChoice_isSubNzAlgebra' 'of' U 'by' <: ]"
:= (SubChoice_isSubNzAlgebra.Build _ _ _ U (subsemialgClosedP _)) (format "[ 'SubChoice_isSubNzAlgebra' 'of' U 'by' <: ]") : form_scope.
Notation
[ 'SubChoice_isSubNzAlgebra' 'of' U 'by' <: ]
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[ "Build", "subsemialgClosedP" ]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addrA
:= @addrA.
Definition
addrA
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addrC
:= @addrC.
Definition
addrC
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
add0r
:= @add0r.
Definition
add0r
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addNr
:= @addNr.
Definition
addNr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addr0
:= addr0.
Definition
addr0
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addrN
:= addrN.
Definition
addrN
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
subrr
:= subrr.
Definition
subrr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addrCA
:= addrCA.
Definition
addrCA
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addrAC
:= addrAC.
Definition
addrAC
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addrACA
:= addrACA.
Definition
addrACA
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addKr
:= addKr.
Definition
addKr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addNKr
:= addNKr.
Definition
addNKr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addrK
:= addrK.
Definition
addrK
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addrNK
:= addrNK.
Definition
addrNK
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
subrK
:= subrK.
Definition
subrK
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
subrKC
:= subrKC.
Definition
subrKC
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
subKr
:= subKr.
Definition
subKr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addrI
:= @addrI.
Definition
addrI
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addIr
:= @addIr.
Definition
addIr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
subrI
:= @subrI.
Definition
subrI
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
subIr
:= @subIr.
Definition
subIr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
opprK
:= @opprK.
Definition
opprK
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
oppr_inj
:= @oppr_inj.
Definition
oppr_inj
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
oppr0
:= oppr0.
Definition
oppr0
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
oppr_eq0
:= oppr_eq0.
Definition
oppr_eq0
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
opprD
:= opprD.
Definition
opprD
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
opprB
:= opprB.
Definition
opprB
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addrKA
:= addrKA.
Definition
addrKA
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
subrKA
:= subrKA.
Definition
subrKA
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
subr0
:= subr0.
Definition
subr0
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
sub0r
:= sub0r.
Definition
sub0r
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
subr_eq
:= subr_eq.
Definition
subr_eq
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addr0_eq
:= addr0_eq.
Definition
addr0_eq
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
subr0_eq
:= subr0_eq.
Definition
subr0_eq
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
subr_eq0
:= subr_eq0.
Definition
subr_eq0
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
addr_eq0
:= addr_eq0.
Definition
addr_eq0
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
eqr_opp
:= eqr_opp.
Definition
eqr_opp
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
eqr_oppLR
:= eqr_oppLR.
Definition
eqr_oppLR
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
sumrN
:= sumrN.
Definition
sumrN
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
sumrB
:= sumrB.
Definition
sumrB
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
sumrMnl
:= sumrMnl.
Definition
sumrMnl
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
sumrMnr
:= sumrMnr.
Definition
sumrMnr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
sumr_const
:= sumr_const.
Definition
sumr_const
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
sumr_const_nat
:= sumr_const_nat.
Definition
sumr_const_nat
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
telescope_sumr
:= telescope_sumr.
Definition
telescope_sumr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
telescope_sumr_eq
:= @telescope_sumr_eq.
Definition
telescope_sumr_eq
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulr0n
:= mulr0n.
Definition
mulr0n
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulr1n
:= mulr1n.
Definition
mulr1n
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulr2n
:= mulr2n.
Definition
mulr2n
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulrS
:= mulrS.
Definition
mulrS
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d
mulrSr
:= mulrSr.
Definition
mulrSr
algebra.algebraic_hierarchy
algebra/algebraic_hierarchy/rings_modules_and_algebras.v
[ "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "eqtype", "ssrnat", "div", "seq", "choice", "fintype", "finfun", "bigop", "prime", "binomial", "nmodule", "Algebra", "Monoid.Theory", "Scale.Exports", "AllExports", "ClosedExports" ]
[]
https://github.com/math-comp/math-comp
91d97df9cf3204b4dab84f4e24bc633e84b6473d