Theorems · Theorem · commutative algebra
RingCon.mapGen_apply_apply_of_surjective
∀ {M : Type u_1} {N : Type u_2} [inst : NonAssocSemiring M] [inst_1 : NonAssocSemiring N] {c : RingCon M} (f : M →+* N),
RingCon.ker f ≤ c → Function.Surjective ⇑f → ∀ {x y : M}, (RingCon.mapGen ⇑f) (f x) (f y) ↔ c x y- Defined in
- Mathlib.RingTheory.Congruence.Hom
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- RingHomstatement and proof · cited by 10,189
- NonAssocSemiringstatement and proof · cited by 805
- RingConstatement and proof · cited by 219
- RingCon.kerstatement and proof · cited by 47
- RingCon.transproof · cited by 3
- RingCon.mapGenstatement · cited by 2
- Relation.map_applyproof · cited by 2
- RingCon.mapGen_eq_map_of_surjectiveproof · cited by 1
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