fact
stringlengths 8
1.54k
| type
stringclasses 19
values | library
stringclasses 8
values | imports
listlengths 1
10
| filename
stringclasses 98
values | symbolic_name
stringlengths 1
42
| docstring
stringclasses 1
value |
|---|---|---|---|---|---|---|
F0:= mkFcube 0.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
F0
| |
F1:= mkFcube 1.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
F1
| |
F2:= mkFcube 2.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
F2
| |
F3:= mkFcube 3.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
F3
| |
F4:= mkFcube 4.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
F4
| |
F5:= mkFcube 5.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
F5
| |
S05:= [:: F0; F4; F3; F2; F1; F5].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S05
| |
S05f(sc : cube) : cube := tnth [tuple of S05] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S05f
| |
S14:= [:: F5; F1; F3; F2; F4; F0].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S14
| |
S14f(sc : cube) : cube := tnth [tuple of S14] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S14f
| |
S23:= [:: F5; F4; F2; F3; F1; F0].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S23
| |
S23f(sc : cube) : cube := tnth [tuple of S23] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S23f
| |
R05:= [:: F0; F2; F4; F1; F3; F5].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R05
| |
R05f(sc : cube) : cube := tnth [tuple of R05] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R05f
| |
R50:= [:: F0; F3; F1; F4; F2; F5].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R50
| |
R50f(sc : cube) : cube := tnth [tuple of R50] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R50f
| |
R14:= [:: F3; F1; F0; F5; F4; F2].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R14
| |
R14f(sc : cube) : cube := tnth [tuple of R14] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R14f
| |
R41:= [:: F2; F1; F5; F0; F4; F3].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R41
| |
R41f(sc : cube) : cube := tnth [tuple of R41] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R41f
| |
R23:= [:: F1; F5; F2; F3; F0; F4].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R23
| |
R23f(sc : cube) : cube := tnth [tuple of R23] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R23f
| |
R32:= [:: F4; F0; F2; F3; F5; F1].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R32
| |
R32f(sc : cube) : cube := tnth [tuple of R32] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R32f
| |
R024:= [:: F2; F5; F4; F1; F0; F3].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R024
| |
R024f(sc : cube) : cube := tnth [tuple of R024] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R024f
| |
R042:= [:: F4; F3; F0; F5; F2; F1].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R042
| |
R042f(sc : cube) : cube := tnth [tuple of R042] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R042f
| |
R012:= [:: F1; F2; F0; F5; F3; F4].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R012
| |
R012f(sc : cube) : cube := tnth [tuple of R012] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R012f
| |
R021:= [:: F2; F0; F1; F4; F5; F3].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R021
| |
R021f(sc : cube) : cube := tnth [tuple of R021] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R021f
| |
R031:= [:: F3; F0; F4; F1; F5; F2].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R031
| |
R031f(sc : cube) : cube := tnth [tuple of R031] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R031f
| |
R013:= [:: F1; F3; F5; F0; F2; F4].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R013
| |
R013f(sc : cube) : cube := tnth [tuple of R013] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R013f
| |
R043:= [:: F4; F2; F5; F0; F3; F1].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R043
| |
R043f(sc : cube) : cube := tnth [tuple of R043] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R043f
| |
R034:= [:: F3; F5; F1; F4; F0; F2].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R034
| |
R034f(sc : cube) : cube := tnth [tuple of R034] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R034f
| |
S1:= [:: F5; F2; F1; F4; F3; F0].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S1
| |
S1f(sc : cube) : cube := tnth [tuple of S1] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S1f
| |
S2:= [:: F5; F3; F4; F1; F2; F0].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S2
| |
S2f(sc : cube) : cube := tnth [tuple of S2] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S2f
| |
S3:= [:: F1; F0; F3; F2; F5; F4].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S3
| |
S3f(sc : cube) : cube := tnth [tuple of S3] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S3f
| |
S4:= [:: F4; F5; F3; F2; F0; F1].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S4
| |
S4f(sc : cube) : cube := tnth [tuple of S4] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S4f
| |
S5:= [:: F2; F4; F0; F5; F1; F3].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S5
| |
S5f(sc : cube) : cube := tnth [tuple of S5] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S5f
| |
S6:= [::F3; F4; F5; F0; F1; F2].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S6
| |
S6f(sc : cube) : cube := tnth [tuple of S6] sc.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S6f
| |
S1_inv: involutive S1f.
Proof. by move=> z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S1_inv
| |
S2_inv: involutive S2f.
Proof. by move=> z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S2_inv
| |
S3_inv: involutive S3f.
Proof. by move=> z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S3_inv
| |
S4_inv: involutive S4f.
Proof. by move=> z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S4_inv
| |
S5_inv: involutive S5f.
Proof. by move=> z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S5_inv
| |
S6_inv: involutive S6f.
Proof. by move=> z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S6_inv
| |
S05_inj: injective S05f.
Proof. by apply: can_inj S05f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S05_inj
| |
S14_inj: injective S14f.
Proof. by apply: can_inj S14f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S14_inj
| |
S23_inv: involutive S23f.
Proof. by move=> z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
S23_inv
| |
R05_inj: injective R05f.
Proof. by apply: can_inj R50f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R05_inj
| |
R14_inj: injective R14f.
Proof. by apply: can_inj R41f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R14_inj
| |
R23_inj: injective R23f.
Proof. by apply: can_inj R32f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R23_inj
| |
R50_inj: injective R50f.
Proof. by apply: can_inj R05f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R50_inj
| |
R41_inj: injective R41f.
Proof. by apply: can_inj R14f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R41_inj
| |
R32_inj: injective R32f.
Proof. by apply: can_inj R23f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R32_inj
| |
R024_inj: injective R024f.
Proof. by apply: can_inj R042f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R024_inj
| |
R042_inj: injective R042f.
Proof. by apply: can_inj R024f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R042_inj
| |
R012_inj: injective R012f.
Proof. by apply: can_inj R021f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R012_inj
| |
R021_inj: injective R021f.
Proof. by apply: can_inj R012f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R021_inj
| |
R031_inj: injective R031f.
Proof. by apply: can_inj R013f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R031_inj
| |
R013_inj: injective R013f.
Proof. by apply: can_inj R031f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R013_inj
| |
R043_inj: injective R043f.
Proof. by apply: can_inj R034f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R043_inj
| |
R034_inj: injective R034f.
Proof. by apply: can_inj R043f _ => z; apply/eqP; case: z; do 6?case. Qed.
|
Lemma
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
R034_inj
| |
id3:= 1 : {perm cube}.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
id3
| |
s05:= (perm S05_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
s05
| |
s14: {perm cube}.
Proof.
apply: (@perm _ S14f); apply: can_inj S14f _ => z.
by apply/eqP; case: z; do 6?case.
Defined.
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
s14
| |
s23:= (perm (inv_inj S23_inv)).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
s23
| |
r05:= (perm R05_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r05
| |
r14:= (perm R14_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r14
| |
r23:= (perm R23_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r23
| |
r50:= (perm R50_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r50
| |
r41:= (perm R41_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r41
| |
r32:= (perm R32_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r32
| |
r024:= (perm R024_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r024
| |
r042:= (perm R042_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r042
| |
r012:= (perm R012_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r012
| |
r021:= (perm R021_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r021
| |
r031:= (perm R031_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r031
| |
r013:= (perm R013_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r013
| |
r043:= (perm R043_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r043
| |
r034:= (perm R034_inj).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
r034
| |
s1:= (perm (inv_inj S1_inv)).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
s1
| |
s2:= (perm (inv_inj S2_inv)).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
s2
| |
s3:= (perm (inv_inj S3_inv)).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
s3
| |
s4:= (perm (inv_inj S4_inv)).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
s4
| |
s5:= (perm (inv_inj S5_inv)).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
s5
| |
s6:= (perm (inv_inj S6_inv)).
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
s6
| |
dir_iso3:= [set p |
[|| id3 == p, s05 == p, s14 == p, s23 == p, r05 == p, r14 == p, r23 == p,
r50 == p, r41 == p, r32 == p, r024 == p, r042 == p, r012 == p, r021 == p,
r031 == p, r013 == p, r043 == p, r034 == p,
s1 == p, s2 == p, s3 == p, s4 == p, s5 == p | s6 == p]].
|
Definition
|
solvable
|
[
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq div",
"From mathcomp Require Import choice fintype tuple finfun bigop finset fingroup",
"From mathcomp Require Import action perm primitive_action ssrAC"
] |
solvable/burnside_app.v
|
dir_iso3
|
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