Theorems · Theorem · commutative algebra
Ideal.mem_map_of_equiv
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] {E : Type u_4} [inst_2 : EquivLike E R S]
[RingEquivClass E R S] (e : E) {I : Ideal R} (y : S), y ∈ Ideal.map e I ↔ ∃ x ∈ I, e x = y- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
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Cites14
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
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- Equiv.symmproof · cited by 3,681
- Ideal.mapstatement and proof · cited by 692
- RingEquiv.symmproof · cited by 567
- Ideal.comapproof · cited by 443
- Equiv.apply_symm_applyproof · cited by 346
- EquivLikestatement and proof · cited by 165
- EquivLike.toEquivproof · cited by 125
- Ideal.mem_map_of_memproof · cited by 71
- RingEquivClass.toRingEquivproof · cited by 12
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