Theorems · Theorem · commutative algebra
RingCon.comap_injective
∀ {R : Type u_3} {R' : Type u_4} [inst : Add R] [inst_1 : Mul R] [inst_2 : Add R'] [inst_3 : Mul R'] {F : Type u_5}
[inst_4 : FunLike F R' R] [inst_5 : MulHomClass F R' R] [inst_6 : AddHomClass F R' R] (f : F),
Function.Surjective ⇑f → Function.Injective fun x => x.comap f- Defined in
- Mathlib.RingTheory.Congruence.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- FunLikestatement and proof · cited by 2,560
- map_mulproof · cited by 1,137
- RingConstatement · cited by 219
- Function.Injective.of_compproof · cited by 82
- MulHomClassstatement and proof · cited by 73
- AddHomClassstatement and proof · cited by 65
- RingCon.comapstatement · cited by 32
- RingCon.toCon_injectiveproof · cited by 2
- Con.comap_injectiveproof · cited by 1
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