ring_ker_quot_mul_mk

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 (a : R), forall (b : R), @Eq.{succ u} (@RingKerQuot.{u,v} R S f) (@RingKerQuotMul.{u,v} R zeroR oneR addR negR subR mulR S zeroS oneS addS negS subS mulS f hom_args (@RingKerQuotMk.{u,v} R S f a) (@RingKerQuotMk.{u,v} R S f b)) (@RingKerQuotMk.{u,v} R S f (mulR a b))

theorem ring_ker_quot_mul_mk.{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 (a : R), forall (b : R), @Eq.{succ u} (@RingKerQuot.{u,v} R S f) (@RingKerQuotMul.{u,v} R zeroR oneR addR negR subR mulR S zeroS oneS addS negS subS mulS f hom_args (@RingKerQuotMk.{u,v} R S f a) (@RingKerQuotMk.{u,v} R S f b)) (@RingKerQuotMk.{u,v} R S f (mulR a b)) :=
  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 => fun a => fun b => @Eq.refl.{succ u} (@RingKerQuot.{u,v} R S f) (@RingKerQuotMk.{u,v} R S f (mulR a b))