statement stringlengths 1 4.33k | proof stringlengths 0 37.9k | type stringclasses 25
values | symbolic_name stringlengths 1 67 | library stringclasses 10
values | filename stringclasses 112
values | imports listlengths 2 138 | deps listlengths 0 64 | docstring stringclasses 798
values | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
pchar_lalg | := pchar_lalg. | Definition | pchar_lalg | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rpredMr | := rpredMr. | Definition | rpredMr | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rpredMl | := rpredMl. | Definition | rpredMl | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rpred_divr | := rpred_divr. | Definition | rpred_divr | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rpred_divl | := rpred_divl. | Definition | rpred_divl | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
divringClosedP | := divringClosedP. | Definition | divringClosedP | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
unitrM | := unitrM. | Definition | unitrM | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
unitr_prodP | := unitr_prodP. | Definition | unitr_prodP | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
prodrV | := prodrV. | Definition | prodrV | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
unitrPr {R x} | := @unitrPr R x. | Definition | unitrPr | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
expr_div_n | := expr_div_n. | Definition | expr_div_n | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulr1_eq | := mulr1_eq. | Definition | mulr1_eq | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
divr1_eq | := divr1_eq. | Definition | divr1_eq | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
divKr | := divKr. | Definition | divKr | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulf_eq0 | := mulf_eq0. | Definition | mulf_eq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
prodf_eq0 | := prodf_eq0. | Definition | prodf_eq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
prodf_seq_eq0 | := prodf_seq_eq0. | Definition | prodf_seq_eq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulf_neq0 | := mulf_neq0. | Definition | mulf_neq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
prodf_neq0 | := prodf_neq0. | Definition | prodf_neq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
prodf_seq_neq0 | := prodf_seq_neq0. | Definition | prodf_seq_neq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
expf_eq0 | := expf_eq0. | Definition | expf_eq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
sqrf_eq0 | := sqrf_eq0. | Definition | sqrf_eq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
expf_neq0 | := expf_neq0. | Definition | expf_neq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
natf_neq0_pchar | := natf_neq0_pchar. | Definition | natf_neq0_pchar | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
natf0_pchar | := natf0_pchar. | Definition | natf0_pchar | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pcharf'_nat | := pcharf'_nat. | Definition | pcharf'_nat | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pcharf0P | := pcharf0P. | Definition | pcharf0P | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eqf_sqr | := eqf_sqr. | Definition | eqf_sqr | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulfI | := mulfI. | Definition | mulfI | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulIf | := mulIf. | Definition | mulIf | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
divfI | := divfI. | Definition | divfI | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
divIf | := divIf. | Definition | divIf | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
sqrf_eq1 | := sqrf_eq1. | Definition | sqrf_eq1 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
expfS_eq1 | := expfS_eq1. | Definition | expfS_eq1 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fieldP | := @fieldP. | Definition | fieldP | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
unitfE | := unitfE. | Definition | unitfE | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulVf | := mulVf. | Definition | mulVf | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulfV | := mulfV. | Definition | mulfV | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
divff | := divff. | Definition | divff | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulKf | := mulKf. | Definition | mulKf | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulVKf | := mulVKf. | Definition | mulVKf | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulfK | := mulfK. | Definition | mulfK | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulfVK | := mulfVK. | Definition | mulfVK | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
divfK | := divfK. | Definition | divfK | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
divKf | := divKf. | Definition | divKf | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
invfM | := invfM. | Definition | invfM | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
invf_div | := invf_div. | Definition | invf_div | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
expfB_cond | := expfB_cond. | Definition | expfB_cond | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
expfB | := expfB. | Definition | expfB | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
prodfV | := prodfV. | Definition | prodfV | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
prodf_div | := prodf_div. | Definition | prodf_div | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
telescope_prodf | := telescope_prodf. | Definition | telescope_prodf | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
telescope_prodf_eq | := @telescope_prodf_eq. | Definition | telescope_prodf_eq | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
addf_div | := addf_div. | Definition | addf_div | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulf_div | := mulf_div. | Definition | mulf_div | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eqr_div | := eqr_div. | Definition | eqr_div | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eqr_sum_div | := eqr_sum_div. | Definition | eqr_sum_div | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pchar0_natf_div | := pchar0_natf_div. | Definition | pchar0_natf_div | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fpredMr | := fpredMr. | Definition | fpredMr | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fpredMl | := fpredMl. | Definition | fpredMl | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fpred_divr | := fpred_divr. | Definition | fpred_divr | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fpred_divl | := fpred_divl. | Definition | fpred_divl | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rmorph_unit | := rmorph_unit. | Definition | rmorph_unit | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rmorphV | := rmorphV. | Definition | rmorphV | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rmorph_div | := rmorph_div. | Definition | rmorph_div | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fmorph_eq0 | := fmorph_eq0. | Definition | fmorph_eq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fmorph_inj | := @fmorph_inj. | Definition | fmorph_inj | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fmorph_eq | := fmorph_eq. | Definition | fmorph_eq | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fmorph_eq1 | := fmorph_eq1. | Definition | fmorph_eq1 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fmorph_pchar | := fmorph_pchar. | Definition | fmorph_pchar | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fmorph_unit | := fmorph_unit. | Definition | fmorph_unit | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fmorphV | := fmorphV. | Definition | fmorphV | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fmorph_div | := fmorph_div. | Definition | fmorph_div | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scaler_eq0 | := scaler_eq0. | Definition | scaler_eq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scalerK | := scalerK. | Definition | scalerK | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scalerKV | := scalerKV. | Definition | scalerKV | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scalerI | := scalerI. | Definition | scalerI | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scaler_injl | := scaler_injl. | Definition | scaler_injl | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
scaler_unit | := scaler_unit. | Definition | scaler_unit | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
invrZ | := invrZ. | Definition | invrZ | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x ^-1" | := (inv x) : ring_scope. | Notation | x ^-1 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [
"inv"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x ^- n" | := (inv (x ^+ n)) : ring_scope. | Notation | x ^- n | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [
"inv"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x / y" | := (mul x y^-1) : ring_scope. | Notation | x / y | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [
"mul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pair_unitr | :=
[qualify a x : R1 * R2 | (x.1 \is a GRing.unit) && (x.2 \is a GRing.unit)]. | Definition | pair_unitr | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [
"R1",
"R2",
"unit"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pair_invr x | :=
if x \is a pair_unitr then (x.1^-1, x.2^-1) else x. | Definition | pair_invr | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [
"pair_unitr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pair_mulVl : {in pair_unitr, left_inverse 1 pair_invr *%R}. | Proof.
rewrite /pair_invr=> x; case: ifP => // /andP[Ux1 Ux2] _.
by congr (_, _); apply: mulVr.
Qed. | Lemma | pair_mulVl | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [
"apply",
"mulVr",
"pair_invr",
"pair_unitr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pair_mulVr : {in pair_unitr, right_inverse 1 pair_invr *%R}. | Proof.
rewrite /pair_invr=> x; case: ifP => // /andP[Ux1 Ux2] _.
by congr (_, _); apply: mulrV.
Qed. | Lemma | pair_mulVr | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [
"apply",
"mulrV",
"pair_invr",
"pair_unitr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pair_unitP x y : y * x = 1 /\ x * y = 1 -> x \is a pair_unitr. | Proof.
case=> [[y1x y2x] [x1y x2y]]; apply/andP.
by split; apply/unitrP; [exists y.1 | exists y.2].
Qed. | Lemma | pair_unitP | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [
"apply",
"pair_unitr",
"split",
"unitrP"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pair_invr_out : {in [predC pair_unitr], pair_invr =1 id}. | Proof. by rewrite /pair_invr => x /negPf/= ->. Qed. | Lemma | pair_invr_out | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [
"id",
"pair_invr",
"pair_unitr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulVb (b : bool) : b != 0 -> b * b = 1. | Proof. by case: b. Qed. | Fact | mulVb | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | Algebraic structure of bool | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
invb_out (x y : bool) : y * x = 1 -> x != 0. | Proof. by case: x; case: y. Qed. | Fact | invb_out | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
bool_fieldP : Field.axiom bool. | Proof. by []. Qed. | Lemma | bool_fieldP | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/divalg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"div",
"choice",
"fintype",
"bigop",
"prime",
"nmodule",
"rings_modules_and_algebras",
"GRing",
"GRing.Theory",
"AllExports",
"ClosedExports"
] | [
"axiom"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
exp R x n | := iterop n (@mul R) x (@one R). | Definition | exp | 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"
] | [
"iterop",
"mul",
"one"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
comm R x y | := @mul R x y = mul y x. | Definition | 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"
] | [
"mul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lreg R x | := injective (@mul R x). | Definition | lreg | 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"
] | [
"mul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rreg R x | := injective ((@mul R)^~ x). | Definition | rreg | 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"
] | [
"mul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"1" | := (@one _) : ring_scope. | Notation | 1 | 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"
] | [
"one"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"n %:R" | := (1 *+ n) : ring_scope. | Notation | n %: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"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"*%R" | := (@mul _) : 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"
] | [
"mul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x * y" | := (mul 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"
] | [
"mul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
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