Theorems · Theorem · commutative algebra
Subring.coe_equivMapOfInjective_apply
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] (s : Subring R) (f : R →+* S)
(hf : Function.Injective ⇑f) (x : ↥s), ↑((s.equivMapOfInjective f hf) x) = f ↑x- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
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Cites7
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
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- Subring.mapstatement · cited by 33
- Subring.equivMapOfInjectivestatement · cited by 2
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