NPAへ戻る
Module
Mathlib.Algebra.Group.Quotient.Mul
npa-mathlib
Packages
2
Module
63
Theorem
750
Declarations
1016
信頼境界外の sidecar
Source text や表示 overlay は提示用メタデータです。信頼する証拠は署名済み証明書と checker の結果です。
Theorem
1
Definition
1
Inductive type
0
Axiom
1
Declarations
NormalQuotMulRep
forall (G : Sort succ u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (N : forall (x : G), Prop...
normal_quot_mul_rep_compat
forall (G : Sort succ u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (N : forall (x : G), Prop...
Eq.rec
Hashes
- source
- sha256:8a6d4b5370143d5fef3db0034f8763ef3f8736664bbe66b80dc1925b15514227
- certificateFile
- sha256:541772d27e36bc290e149eb6b1498e659dea43e7d53884b2d828f26e5c9c28b8
- export
- sha256:9570dfe4c8b6ca61fe53acd2bf41cf193be20a4d9118cbc295f1c1a10d602cc7
- axiomReport
- sha256:5bd7339ac208646efb0ed11ff2499737a45b42195bb28180b5685aed4560bbe3
- certificate
- sha256:5495b3aba0eb579efd418b5a86fad16765c2f21889c9531747fa0d152f774013
Source
import Std.Logic.Eq
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Group.Subgroup
import Mathlib.Algebra.Group.Quotient
def NormalQuotMulRep.{u} :
forall (G : Sort succ u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (N : forall (x : G), Prop), forall (group_args : @GroupLawArgs.{succ u} G one mul inv), forall (normal_args : @NormalSubgroupLawArgs.{succ u} G one mul inv N), forall (a : G), forall (b : G), @NormalQuot.{u} G one mul inv N group_args normal_args :=
fun G => fun one => fun mul => fun inv => fun N => fun group_args => fun normal_args => fun a => fun b => @NormalQuotMk.{u} G one mul inv N group_args normal_args (mul a b)
theorem normal_quot_mul_rep_compat.{u} :
forall (G : Sort succ u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (N : forall (x : G), Prop), forall (group_args : @GroupLawArgs.{succ u} G one mul inv), forall (normal_args : @NormalSubgroupLawArgs.{succ u} G one mul inv N), forall (a : G), forall (a2 : G), forall (b : G), forall (b2 : G), forall (ha : @NormalRel.{succ u} G one mul inv N a a2), forall (hb : @NormalRel.{succ u} G one mul inv N b b2), @Eq.{succ u} (@NormalQuot.{u} G one mul inv N group_args normal_args) (@NormalQuotMulRep.{u} G one mul inv N group_args normal_args a b) (@NormalQuotMulRep.{u} G one mul inv N group_args normal_args a2 b2) :=
fun G => fun one => fun mul => fun inv => fun N => fun group_args => fun normal_args => fun a => fun a2 => fun b => fun b2 => fun ha => fun hb => @normal_quot_sound.{u} G one mul inv N group_args normal_args (mul a b) (mul a2 b2) (@normal_rel_mul_compat.{succ u} G one mul inv group_args N normal_args a a2 b b2 ha hb)