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Declaration
ring_image_one
Mathlib.Algebra.Ring.FirstIsomorphism.Basic
Packages
2
Module
63
Theorem
750
Declarations
1016
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Statement
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), @RingImagePred.{u,v} R S f oneSProof term
theorem ring_image_one.{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), @RingImagePred.{u,v} R S f oneS :=
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 (P : Prop) => fun (mk : forall (a : R), forall (h : @Eq.{v} S (f a) oneS), P) => mk oneR (@ring_hom_one.{u,v} R zeroR oneR addR negR subR mulR S zeroS oneS addS negS subS mulS f hom_args)