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
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|---|---|---|---|---|---|---|---|---|---|---|
can2_nmod_morphism | := can2_nmod_morphism. | Definition | can2_nmod_morphism | 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 | |
can2_zmod_morphism | := can2_zmod_morphism. | Definition | can2_zmod_morphism | 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 | |
monoid_morphism | := monoid_morphism. | Definition | monoid_morphism | 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 | |
rmorph0 | := rmorph0. | Definition | rmorph0 | 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 | |
rmorphN | := rmorphN. | Definition | rmorphN | 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 | |
rmorphD | := rmorphD. | Definition | rmorphD | 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 | |
rmorphB | := rmorphB. | Definition | rmorphB | 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 | |
rmorph_sum | := rmorph_sum. | Definition | rmorph_sum | 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 | |
rmorphMn | := rmorphMn. | Definition | rmorphMn | 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 | |
rmorphMNn | := rmorphMNn. | Definition | rmorphMNn | 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 | |
rmorphism_monoidP | := rmorphism_monoidP. | Definition | rmorphism_monoidP | 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 | |
rmorph1 | := rmorph1. | Definition | rmorph1 | 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 | |
rmorph_eq1 | := rmorph_eq1. | Definition | rmorph_eq1 | 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 | |
rmorphM | := rmorphM. | Definition | rmorphM | 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 | |
rmorphMsign | := rmorphMsign. | Definition | rmorphMsign | 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 | |
rmorph_nat | := rmorph_nat. | Definition | rmorph_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 | |
rmorph_eq_nat | := rmorph_eq_nat. | Definition | rmorph_eq_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 | |
rmorph_prod | := rmorph_prod. | Definition | rmorph_prod | 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 | |
rmorphXn | := rmorphXn. | Definition | rmorphXn | 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 | |
rmorphN1 | := rmorphN1. | Definition | rmorphN1 | 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 | |
rmorph_sign | := rmorph_sign. | Definition | rmorph_sign | 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 | |
rmorph_pchar | := rmorph_pchar. | Definition | rmorph_pchar | 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 | |
can2_monoid_morphism | := can2_monoid_morphism. | Definition | can2_monoid_morphism | 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 | |
rmorph_comm | := rmorph_comm. | Definition | rmorph_comm | 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 | |
scalerA | := scalerA. | Definition | 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"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scale1r | := @scale1r. | Definition | 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"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scalerDr | := @scalerDr. | Definition | 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"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scalerDl | := @scalerDl. | Definition | 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"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scaler0 | := scaler0. | Definition | scaler0 | 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 | |
scale0r | := @scale0r. | Definition | 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"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scaleNr | := scaleNr. | Definition | scaleNr | 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 | |
scaleN1r | := scaleN1r. | Definition | scaleN1r | 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 | |
scalerN | := scalerN. | Definition | scalerN | 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 | |
scalerBl | := scalerBl. | Definition | scalerBl | 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 | |
scalerBr | := scalerBr. | Definition | scalerBr | 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 | |
scaler_nat | := scaler_nat. | Definition | scaler_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 | |
scalerMnl | := scalerMnl. | Definition | scalerMnl | 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 | |
scalerMnr | := scalerMnr. | Definition | scalerMnr | 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 | |
scaler_suml | := scaler_suml. | Definition | scaler_suml | 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 | |
scaler_sumr | := scaler_sumr. | Definition | scaler_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 | |
scalerAl | := @scalerAl. | Definition | 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"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulr_algl | := mulr_algl. | Definition | mulr_algl | 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 | |
scaler_sign | := scaler_sign. | Definition | scaler_sign | 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 | |
signrZK | := signrZK. | Definition | signrZK | 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 | |
scalerCA | := scalerCA. | Definition | scalerCA | 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 | |
scalerAr | := @scalerAr. | Definition | 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"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulr_algr | := mulr_algr. | Definition | mulr_algr | 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 | |
comm_alg | := comm_alg. | Definition | comm_alg | 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 | |
exprZn | := exprZn. | Definition | exprZn | 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 | |
scaler_prodl | := scaler_prodl. | Definition | scaler_prodl | 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 | |
scaler_prodr | := scaler_prodr. | Definition | scaler_prodr | 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 | |
scaler_prod | := scaler_prod. | Definition | scaler_prod | 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 | |
raddfZnat | := raddfZnat. | Definition | raddfZnat | 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 | |
raddfZsign | := raddfZsign. | Definition | raddfZsign | 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 | |
in_algE | := in_algE. | Definition | in_algE | 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 | |
scalable_for | := scalable_for. | Definition | scalable_for | 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 | |
semilinear_for | := semilinear_for. | Definition | semilinear_for | 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 | |
linear_for | := linear_for. | Definition | linear_for | 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 | |
nmod_morphism_semilinear | := nmod_morphism_semilinear. | Definition | nmod_morphism_semilinear | 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 | |
zmod_morphism_linear | := zmod_morphism_linear. | Definition | zmod_morphism_linear | 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 | |
scalable_semilinear | := scalable_semilinear. | Definition | scalable_semilinear | 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 | |
scalable_linear | := scalable_linear. | Definition | scalable_linear | 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 | |
linear0 | := linear0. | Definition | linear0 | 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 | |
linearN | := linearN. | Definition | linearN | 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 | |
linearD | := linearD. | Definition | linearD | 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 | |
linearB | := linearB. | Definition | linearB | 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 | |
linear_sum | := linear_sum. | Definition | linear_sum | 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 | |
linearMn | := linearMn. | Definition | linearMn | 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 | |
linearMNn | := linearMNn. | Definition | linearMNn | 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 | |
semilinearP | := semilinearP. | Definition | semilinearP | 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 | |
linearP | := linearP. | Definition | linearP | 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 | |
linearZ_LR | := linearZ_LR. | Definition | linearZ_LR | 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 | |
linearZ | := linearZ. | Definition | linearZ | 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 | |
semilinearPZ | := semilinearPZ. | Definition | semilinearPZ | 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 | |
linearPZ | := linearPZ. | Definition | linearPZ | 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 | |
linearZZ | := linearZZ. | Definition | linearZZ | 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 | |
semiscalarP | := semiscalarP. | Definition | semiscalarP | 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 | |
scalarP | := scalarP. | Definition | scalarP | 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 | |
scalarZ | := scalarZ. | Definition | scalarZ | 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 | |
can2_scalable | := can2_scalable. | Definition | can2_scalable | 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 | |
can2_linear | := can2_linear. | Definition | can2_linear | 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 | |
can2_semilinear | := can2_semilinear. | Definition | can2_semilinear | 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 | |
rmorph_alg | := rmorph_alg. | Definition | rmorph_alg | 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 | |
raddf | := (raddf0, raddfN, raddfD, raddfMn). | Definition | raddf | 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"
] | [
"raddf0",
"raddfD",
"raddfMn",
"raddfN"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rmorphE | :=
(rmorphD, rmorph0, rmorphB, rmorphN, rmorphMNn, rmorphMn, rmorph1, rmorphXn). | Definition | rmorphE | 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"
] | [
"rmorph0",
"rmorph1",
"rmorphB",
"rmorphD",
"rmorphMNn",
"rmorphMn",
"rmorphN",
"rmorphXn"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
linearE | :=
(linearD, linear0, linearB, linearMNn, linearMn, linearZ). | Definition | linearE | 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"
] | [
"linear0",
"linearB",
"linearD",
"linearMNn",
"linearMn",
"linearZ"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
null_fun V | := (null_fun V) (only parsing). | Notation | null_fun | 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 | |
in_alg A | := (in_alg A) (only parsing). | Notation | in_alg | 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 | |
Ione | := IOne : Ione. | Variant | Ione | 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 | |
Inatmul | :=
| INatmul : Ione -> nat -> Inatmul
| IOpp : Inatmul -> Inatmul. | Inductive | Inatmul | 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"
] | [
"Ione",
"nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Idummy_placeholder | :=. | Variant | Idummy_placeholder | 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 | |
parse (x : Number.int) : Inatmul | :=
match x with
| Number.IntDecimal (Decimal.Pos u) => INatmul IOne (Nat.of_uint u)
| Number.IntDecimal (Decimal.Neg u) => IOpp (INatmul IOne (Nat.of_uint u))
| Number.IntHexadecimal (Hexadecimal.Pos u) =>
INatmul IOne (Nat.of_hex_uint u)
| Number.IntHexadecimal (Hexadecimal.Neg u) =>
IOpp (INatmu... | Definition | parse | 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"
] | [
"Inatmul",
"int",
"of_hex_uint",
"of_uint"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
print (x : Inatmul) : option Number.int | :=
match x with
| INatmul IOne n =>
Some (Number.IntDecimal (Decimal.Pos (Nat.to_uint n)))
| IOpp (INatmul IOne n) =>
Some (Number.IntDecimal (Decimal.Neg (Nat.to_uint n)))
| _ => None
end. | Definition | print | 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"
] | [
"Inatmul",
"int",
"to_uint"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"0" | := (@zero _) : ring_scope. | Notation | 0 | 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"
] | [
"zero"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"-%R" | := (@opp _) : ring_scope. | Notation | -%R | 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"
] | [
"opp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"- x" | := (opp x) : ring_scope. | Notation | - x | 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"
] | [
"opp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"+%R" | := (@add _) : function_scope. | Notation | +%R | 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"
] | [
"add"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x + y" | := (add x y) : ring_scope. | Notation | x + y | 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"
] | [
"add"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x - y" | := (add x (- y)) : ring_scope. | Notation | x - y | 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"
] | [
"add"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x *+ n" | := (natmul x n) : ring_scope. | Notation | x *+ n | 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"
] | [
"natmul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
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