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 |
|---|---|---|---|---|---|---|---|---|---|---|
"[ 'SubChoice_isSubSemiAlgebra' 'of' U 'by' <: ]" | :=
(SubChoice_isSubNzSemiAlgebra.Build _ _ _ U (subsemialgClosedP _))
(format "[ 'SubChoice_isSubSemiAlgebra' 'of' U 'by' <: ]")
: form_scope. | Notation | [ 'SubChoice_isSubSemiAlgebra' 'of' U 'by' <: ] | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"Build",
"subsemialgClosedP"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"[ 'SubChoice_isSubAlgebra' 'of' U 'by' <: ]" | :=
(SubChoice_isSubNzAlgebra.Build _ _ _ U (subalgClosedP _))
(format "[ 'SubChoice_isSubAlgebra' 'of' U 'by' <: ]")
: form_scope. | Notation | [ 'SubChoice_isSubAlgebra' 'of' U 'by' <: ] | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"Build",
"subalgClosedP"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"[ 'SubRing_isSubUnitRing' 'of' U 'by' <: ]" | :=
(SubNzRing_isSubUnitRing.Build _ _ U (divringClosedP _))
(format "[ 'SubRing_isSubUnitRing' 'of' U 'by' <: ]")
: form_scope. | Notation | [ 'SubRing_isSubUnitRing' 'of' U 'by' <: ] | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"Build",
"divringClosedP"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Nmodule_isSemiRing R | := (Nmodule_isNzSemiRing R) (only parsing). | Notation | Nmodule_isSemiRing | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | Definitions and lemmas | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
addr_closed | := nmod_closed. | Definition | addr_closed | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"nmod_closed"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
zmod_closedD | := zmod_closed0D. | Definition | zmod_closedD | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"zmod_closed0D"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
subr_2closed | := subr_closed. | Definition | subr_2closed | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"subr_closed"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
char | := pchar (only parsing). | Notation | char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
has_char0 L | := (has_pchar0 L) (only parsing). | Notation | has_char0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"has_pchar0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_aut | := pFrobenius_aut (only parsing). | Notation | Frobenius_aut | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_aut"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
charf0 | := pcharf0 (only parsing). | Notation | charf0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pcharf0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
charf_prime | := pcharf_prime (only parsing). | Notation | charf_prime | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pcharf_prime"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrn_char | := mulrn_pchar (only parsing). | Notation | mulrn_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"mulrn_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
natr_mod_char | := natr_mod_pchar (only parsing). | Notation | natr_mod_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"natr_mod_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
dvdn_charf | := dvdn_pcharf (only parsing). | Notation | dvdn_charf | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"dvdn_pcharf"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
charf_eq | := pcharf_eq (only parsing). | Notation | charf_eq | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pcharf_eq"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
bin_lt_charf_0 | := bin_lt_pcharf_0 (only parsing). | Notation | bin_lt_charf_0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"bin_lt_pcharf_0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autE | := pFrobenius_autE (only parsing). | Notation | Frobenius_autE | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_aut0 | := pFrobenius_aut0 (only parsing). | Notation | Frobenius_aut0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_aut0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_aut1 | := pFrobenius_aut1 (only parsing). | Notation | Frobenius_aut1 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_aut1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autD_comm | := pFrobenius_autD_comm (only parsing). | Notation | Frobenius_autD_comm | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autD_comm"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autMn | := pFrobenius_autMn (only parsing). | Notation | Frobenius_autMn | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autMn"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_aut_nat | := pFrobenius_aut_nat (only parsing). | Notation | Frobenius_aut_nat | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_aut_nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autM_comm | := pFrobenius_autM_comm (only parsing). | Notation | Frobenius_autM_comm | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autM_comm"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autX | := pFrobenius_autX (only parsing). | Notation | Frobenius_autX | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autX"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
addrr_char2 | := addrr_pchar2 (only parsing). | Notation | addrr_char2 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"addrr_pchar2"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autN | := pFrobenius_autN (only parsing). | Notation | Frobenius_autN | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autN"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autB_comm | := pFrobenius_autB_comm (only parsing). | Notation | Frobenius_autB_comm | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autB_comm"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
exprNn_char | := exprNn_pchar (only parsing). | Notation | exprNn_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"exprNn_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
oppr_char2 | := oppr_pchar2 (only parsing). | Notation | oppr_char2 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"oppr_pchar2"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
subr_char2 | := subr_pchar2 (only parsing). | Notation | subr_char2 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"subr_pchar2"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
addrK_char2 | := addrK_pchar2 (only parsing). | Notation | addrK_char2 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"addrK_pchar2"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
addKr_char2 | := addKr_pchar2 (only parsing). | Notation | addKr_char2 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"addKr_pchar2"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
multiplicative (R S : pzSemiRingType) (f : R -> S) : Prop | :=
{morph f : x y / x * y}%R * (f 1 = 1). | Definition | multiplicative | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rmorphismMP (R S : pzSemiRingType) (f : {rmorphism R -> S}) :
multiplicative f | := (fun p => (p.2, p.1)) (rmorphism_monoidP f). | Definition | rmorphismMP | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"multiplicative",
"rmorphism_monoidP"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rmorph_char | := rmorph_pchar (only parsing). | Notation | rmorph_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"rmorph_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
additive_linear | := zmod_morphism_linear. | Definition | additive_linear | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"zmod_morphism_linear"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pFrobenius_aut_is_multiplicative | :=
(fun p => (p.2, p.1) \o pFrobenius_aut_is_monoid_morphism) (only parsing). | Notation | pFrobenius_aut_is_multiplicative | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_aut_is_monoid_morphism"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
exprDn_char | := exprDn_pchar (only parsing). | Notation | exprDn_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"exprDn_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
natf_neq0 | := natf_neq0_pchar (only parsing). | Notation | natf_neq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"natf_neq0_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
natf0_char | := natf0_pchar (only parsing). | Notation | natf0_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"natf0_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
charf'_nat | := pcharf'_nat (only parsing). | Notation | charf'_nat | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pcharf'_nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
charf0P | := pcharf0P (only parsing). | Notation | charf0P | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pcharf0P"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
char0_natf_div | := pchar0_natf_div (only parsing). | Notation | char0_natf_div | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pchar0_natf_div"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fmorph_char | := fmorph_pchar (only parsing). | Notation | fmorph_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"fmorph_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
char_lalg | := pchar_lalg (only parsing). | Notation | char_lalg | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pchar_lalg"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lalgMixin
(R : pzRingType) (A : pzLalgType R) (B : lmodType R) (f : B -> A) :
phant B -> injective f -> scalable f ->
forall mulB, {morph f : x y / mulB x y >-> x * y} ->
forall a u v, a *: (mulB u v) = mulB (a *: u) v. | Proof.
by move=> _ injf fZ mulB fM a x y; apply: injf; rewrite !(fZ, fM) scalerAl.
Qed. | Lemma | lalgMixin | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"apply",
"fM",
"injf",
"scalable",
"scalerAl"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
comRingMixin (R : comPzRingType) (T : pzRingType) (f : T -> R) :
phant T -> injective f -> {morph f : x y / x * y} -> commutative (@mul T). | Proof. by move=> _ inj_f fM x y; apply: inj_f; rewrite !fM mulrC. Qed. | Lemma | comRingMixin | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"apply",
"fM",
"inj_f",
"mul",
"mulrC"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
algMixin
(R : pzRingType) (A : pzAlgType R) (B : pzLalgType R) (f : B -> A) :
phant B -> injective f -> {morph f : x y / x * y} -> scalable f ->
forall k (x y : B), k *: (x * y) = x * (k *: y). | Proof.
by move=> _ inj_f fM fZ a x y; apply: inj_f; rewrite !(fM, fZ) scalerAr.
Qed. | Lemma | algMixin | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"apply",
"fM",
"inj_f",
"scalable",
"scalerAr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
charf0 | := pcharf0. | Definition | charf0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pcharf0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
charf_prime | := pcharf_prime. | Definition | charf_prime | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pcharf_prime"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mulrn_char | := mulrn_pchar. | Definition | mulrn_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"mulrn_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
dvdn_charf | := dvdn_pcharf. | Definition | dvdn_charf | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"dvdn_pcharf"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
charf_eq | := pcharf_eq. | Definition | charf_eq | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pcharf_eq"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
bin_lt_charf_0 | := bin_lt_pcharf_0. | Definition | bin_lt_charf_0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"bin_lt_pcharf_0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autE | := pFrobenius_autE. | Definition | Frobenius_autE | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_aut0 | := pFrobenius_aut0. | Definition | Frobenius_aut0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_aut0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_aut1 | := pFrobenius_aut1. | Definition | Frobenius_aut1 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_aut1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autD_comm | := pFrobenius_autD_comm. | Definition | Frobenius_autD_comm | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autD_comm"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autMn | := pFrobenius_autMn. | Definition | Frobenius_autMn | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autMn"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_aut_nat | := pFrobenius_aut_nat. | Definition | Frobenius_aut_nat | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_aut_nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autM_comm | := pFrobenius_autM_comm. | Definition | Frobenius_autM_comm | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autM_comm"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autX | := pFrobenius_autX. | Definition | Frobenius_autX | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autX"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autN | := pFrobenius_autN. | Definition | Frobenius_autN | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autN"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Frobenius_autB_comm | := pFrobenius_autB_comm. | Definition | Frobenius_autB_comm | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pFrobenius_autB_comm"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
exprNn_char | := exprNn_pchar. | Definition | exprNn_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"exprNn_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
addrr_char2 | := addrr_pchar2. | Definition | addrr_char2 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"addrr_pchar2"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
oppr_char2 | := oppr_pchar2. | Definition | oppr_char2 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"oppr_pchar2"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
addrK_char2 | := addrK_pchar2. | Definition | addrK_char2 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"addrK_pchar2"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
addKr_char2 | := addKr_pchar2. | Definition | addKr_char2 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"addKr_pchar2"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
exprDn_char | := exprDn_pchar. | Definition | exprDn_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"exprDn_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
semi_additive | := semi_additive. | Definition | semi_additive | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
additive | := additive. | Definition | additive | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
can2_semi_additive | := can2_semi_additive. | Definition | can2_semi_additive | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
can2_additive | := can2_additive. | Definition | can2_additive | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
multiplicative | := multiplicative. | Definition | multiplicative | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rmorphismMP | := rmorphismMP. | Definition | rmorphismMP | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rmorph_char | := rmorph_pchar. | Definition | rmorph_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"rmorph_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
can2_rmorphism | := can2_rmorphism. | Definition | can2_rmorphism | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
additive_semilinear | := additive_semilinear. | Definition | additive_semilinear | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
additive_linear | := additive_linear. | Definition | additive_linear | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
char_lalg | := pchar_lalg. | Definition | char_lalg | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pchar_lalg"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
natf_neq0 | := natf_neq0_pchar. | Definition | natf_neq0 | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"natf_neq0_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
natf0_char | := natf0_pchar. | Definition | natf0_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"natf0_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
charf'_nat | := pcharf'_nat. | Definition | charf'_nat | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pcharf'_nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
charf0P | := pcharf0P. | Definition | charf0P | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pcharf0P"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
char0_natf_div | := pchar0_natf_div. | Definition | char0_natf_div | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"pchar0_natf_div"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
fmorph_char | := fmorph_pchar. | Definition | fmorph_char | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [
"fmorph_pchar"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
semiRingType | := (nzSemiRingType) (only parsing). | Notation | semiRingType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ringType | := (nzRingType) (only parsing). | Notation | ringType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
comSemiRingType | := (comNzSemiRingType) (only parsing). | Notation | comSemiRingType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
comRingType | := (comNzRingType) (only parsing). | Notation | comRingType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
subSemiRingType | := (subNzSemiRingType) (only parsing). | Notation | subSemiRingType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
subComSemiRingType | := (subComNzSemiRingType) (only parsing). | Notation | subComSemiRingType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
subRingType | := (subNzRingType) (only parsing). | Notation | subRingType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
subComRingType | := (subComNzRingType) (only parsing). | Notation | subComRingType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lSemiAlgType | := (nzLSemiAlgType) (only parsing). | Notation | lSemiAlgType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lalgType | := (nzLalgType) (only parsing). | Notation | lalgType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
semiAlgType | := (nzSemiAlgType) (only parsing). | Notation | semiAlgType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
algType | := (nzAlgType) (only parsing). | Notation | algType | algebra.algebraic_hierarchy | algebra/algebraic_hierarchy/ssralg.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"div",
"seq",
"choice",
"fintype",
"finfun",
"bigop",
"prime",
"binomial",
"nmodule",
"rings_modules_and_algebras",
"divalg",
"decfield",
"GRing",
"GRing.Theory",
"AllExports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
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