Declaration
third_iso_phi_mul
Mathlib.Algebra.Group.ThirdIsomorphism
Packages
2
Module
63
Theorems
750
Declarations
1016
Untrusted sidecar
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Statement
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 (Hpred : forall (x : G), Prop), forall (group_args : @GroupLawArgs.{succ u} G one mul inv), forall (n_normal : @NormalSubgroupLawArgs.{succ u} G one mul inv N), forall (h_normal : @NormalSubgroupLawArgs.{succ u} G one mul inv Hpred), forall (n_le_h : forall (x : G), forall (hn : N x), Hpred x), forall (a : G), forall (b : G), @Eq.{succ u} (@NormalQuot.{u} G one mul inv Hpred group_args h_normal) (@ThirdIsoPhi.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h (@NormalQuotMk.{u} G one mul inv N group_args n_normal (mul a b))) (@NormalQuotMul.{u} G one mul inv Hpred group_args h_normal (@ThirdIsoPhi.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h (@NormalQuotMk.{u} G one mul inv N group_args n_normal a)) (@ThirdIsoPhi.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h (@NormalQuotMk.{u} G one mul inv N group_args n_normal b)))
Proof term
fun G => fun one => fun mul => fun inv => fun N => fun Hpred => fun group_args => fun n_normal => fun h_normal => fun n_le_h => fun a => fun b => @Eq.refl.{succ u} (@NormalQuot.{u} G one mul inv Hpred group_args h_normal) (@NormalQuotMk.{u} G one mul inv Hpred group_args h_normal (mul a b))
Constants
Mathlib.Algebra.Group.Basic.GroupLawArgs
Interface hash: sha256:2d87332e5e2af4c4567f00f441f3a30fa8780563655728bc695cf467701fd8db
Mathlib.Algebra.Group.Quotient.NormalQuot
Interface hash: sha256:ac0d31805001e1ea1fe46e644b7187eb3e256364063df8dec29e9007eb5b31e4
Mathlib.Algebra.Group.Quotient.NormalQuotMk
Interface hash: sha256:4a730a1db38d5b5362787ead7697f2eff1ea187c9a89ef87923ebc0d611bfd41
Mathlib.Algebra.Group.Quotient.Group.NormalQuotMul
Interface hash: sha256:95284af9f36887cea051b9a93b81e820a0a72e0051f49a837fe897a74c13ee7f
Mathlib.Algebra.Group.Subgroup.NormalSubgroupLawArgs
Interface hash: sha256:808ae35e6b38f18f2fa58c14eebebbc2e93b11d1887b258bff2cea4daf9d9fb8
Mathlib.Algebra.Group.ThirdIsomorphism.ThirdIsoPhi
Interface hash: sha256:16e7f503b813ca8bd20fba0532ccdb711aafc82cd806ff00d62bcaf621f3718e
Std.Logic.Eq.Eq
Interface hash: sha256:ca4f8520fd678a809c3ebf0bc7fa38d3063ca4d231e79d567de888685449a015