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声明
ring_image_neg_closed
Mathlib.Algebra.Ring.FirstIsomorphism.Basic
包
2
模块
63
定理
750
声明
1016
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陈述
forall (R : Sort 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 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.{u,v} R zeroR oneR addR negR subR mulR S zeroS oneS addS negS subS mulS f), forall (y : S), forall (hy : @RingImagePred.{u,v} R S f y), @RingImagePred.{u,v} R S f (negS y)证明项
theorem ring_image_neg_closed.{u,v} :
forall (R : Sort 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 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.{u,v} R zeroR oneR addR negR subR mulR S zeroS oneS addS negS subS mulS f), forall (y : S), forall (hy : @RingImagePred.{u,v} R S f y), @RingImagePred.{u,v} R S f (negS y) :=
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 y => fun hy => hy (@RingImagePred.{u,v} R S f (negS y)) (fun (a : R) => fun (hay : @Eq.{v} S (f a) y) => fun (P : Prop) => fun (mk : forall (c : R), forall (h : @Eq.{v} S (f c) (negS y)), P) => mk (negR a) (@eq_trans.{v} S (f (negR a)) (negS (f a)) (negS y) (@ring_hom_neg.{u,v} R zeroR oneR addR negR subR mulR S zeroS oneS addS negS subS mulS f hom_args a) (@eq_congr_arg.{v,v} S S negS (f a) y hay)))