Theorems · Theorem · commutative algebra
RingEquiv.ofLeftInverseS_symm_apply
∀ {R : Type u} {S : Type v} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S] {g : S → R} {f : R →+* S}
(h : Function.LeftInverse g ⇑f) (x : ↥f.rangeS), (RingEquiv.ofLeftInverseS h).symm x = g ↑x- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 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
- RingEquivstatement · cited by 1,147
- NonAssocSemiringstatement and proof · cited by 805
- RingEquiv.symmstatement · cited by 567
- Subsemiringstatement · cited by 456
- RingHom.rangeSstatement and proof · cited by 47
- RingEquiv.ofLeftInverseSstatement · cited by 2
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