RingKerQuotMul

Mathlib.Algebra.Ring.FirstIsomorphism

Packages

Module

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。

Statement

forall (R : Sort succ u), forall (zeroR : R), forall (oneR : R), forall (addR : forall (a : R), forall (b : R), R), forall (negR : forall (a : R), R), forall (subR : forall (a : R), forall (b : R), R), forall (mulR : forall (a : R), forall (b : R), R), forall (S : Sort succ v), forall (zeroS : S), forall (oneS : S), forall (addS : forall (a : S), forall (b : S), S), forall (negS : forall (a : S), S), forall (subS : forall (a : S), forall (b : S), S), forall (mulS : forall (a : S), forall (b : S), S), forall (f : forall (x : R), S), forall (hom_args : @RingHomLawArgs.{succ u,succ v} R zeroR oneR addR negR subR mulR S zeroS oneS addS negS subS mulS f), forall (q1 : @RingKerQuot.{u,v} R S f), forall (q2 : @RingKerQuot.{u,v} R S f), @RingKerQuot.{u,v} R S f

Proof term

def RingKerQuotMul.{u,v} :
  forall (R : Sort succ u), forall (zeroR : R), forall (oneR : R), forall (addR : forall (a : R), forall (b : R), R), forall (negR : forall (a : R), R), forall (subR : forall (a : R), forall (b : R), R), forall (mulR : forall (a : R), forall (b : R), R), forall (S : Sort succ v), forall (zeroS : S), forall (oneS : S), forall (addS : forall (a : S), forall (b : S), S), forall (negS : forall (a : S), S), forall (subS : forall (a : S), forall (b : S), S), forall (mulS : forall (a : S), forall (b : S), S), forall (f : forall (x : R), S), forall (hom_args : @RingHomLawArgs.{succ u,succ v} R zeroR oneR addR negR subR mulR S zeroS oneS addS negS subS mulS f), forall (q1 : @RingKerQuot.{u,v} R S f), forall (q2 : @RingKerQuot.{u,v} R S f), @RingKerQuot.{u,v} R S f :=
  fun R => fun zeroR => fun oneR => fun addR => fun negR => fun subR => fun mulR => fun S => fun zeroS => fun oneS => fun addS => fun negS => fun subS => fun mulS => fun f => fun hom_args => @Quotient.lift2.{u,u} R (@RingKerQuot.{u,v} R S f) (@KerSetoid.{u,v} R S f) (@RingKerQuotMulRep.{u,v} R mulR S f) (fun (a : R) => fun (a2 : R) => fun (b : R) => fun (b2 : R) => fun (ha : @Setoid.r.{u} R (@KerSetoid.{u,v} R S f) a a2) => fun (hb : @Setoid.r.{u} R (@KerSetoid.{u,v} R S f) b b2) => @ring_ker_quot_mul_rep_compat.{u,v} R zeroR oneR addR negR subR mulR S zeroS oneS addS negS subS mulS f hom_args a a2 b b2 ha hb)