Theorems · Theorem · commutative algebra
RingHom.mem_rangeS_self
∀ {R : Type u} {S : Type v} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S] (f : R →+* S) (x : R),
f x ∈ f.rangeS- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement · cited by 456
- RingHom.rangeSstatement · cited by 47
- RingHom.mem_rangeSproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- RingHom.rangeSRestrictproof · cited by 4
- RingCon.comapQuotientEquivRangeS_mkstatement · cited by 0
- RingCon.comapQuotientEquivRangeS_symm_mkstatement and proof · cited by 0