Theorems · Theorem · commutative algebra
RingHom.surjective_codRestrict
∀ {R : Type u} {S : Type v} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S] {σS : Type u_2}
[inst_2 : SetLike σS S] [inst_3 : SubsemiringClass σS S] {f : R →+* S} {s : σS} {h : ∀ (x : R), f x ∈ s},
Function.Surjective ⇑(f.codRestrict s h) ↔ f.rangeS = Subsemiring.ofClass s- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- SetLikestatement and proof · cited by 1,084
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement · cited by 456
- RingHom.rangeSstatement · cited by 47
- SubsemiringClassstatement and proof · cited by 30
- SetLike.coe_set_eqproof · cited by 27
- RingHom.codRestrictstatement · cited by 12
- Subsemiring.ofClassstatement · cited by 2
- Set.surjective_codRestrictproof · cited by 1
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