KerSetoid

Mathlib.Algebra.Group.Kernel.Quotient

Packages

Module

Theorems

750

Declarations

1016

Untrusted sidecar

Source text and display overlays are presentation metadata. The signed certificate and checker result are the trusted evidence.

Statement

forall (G : Sort succ u), forall (H : Sort succ v), forall (f : forall (x : G), H), @Setoid.{u} G

Proof term

fun G => fun H => fun f => @Setoid.mk.{u} G (@KerRel.{succ u,succ v} G H f) (fun (P : Prop) => fun (mk_equiv : forall (refl_arg : forall (x : G), @KerRel.{succ u,succ v} G H f x x), forall (symm_arg : forall (x : G), forall (y : G), forall (p : @KerRel.{succ u,succ v} G H f x y), @KerRel.{succ u,succ v} G H f y x), forall (trans_arg : forall (x : G), forall (y : G), forall (z : G), forall (p : @KerRel.{succ u,succ v} G H f x y), forall (q : @KerRel.{succ u,succ v} G H f y z), @KerRel.{succ u,succ v} G H f x z), P) => mk_equiv (@ker_rel_refl.{succ u,succ v} G H f) (@ker_rel_symm.{succ u,succ v} G H f) (@ker_rel_trans.{succ u,succ v} G H f))