Theorems · Theorem · commutative algebra
Ideal.mem_map_of_mem
∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S] (f : F)
{I : Ideal R} {x : R}, x ∈ I → f x ∈ Ideal.map f I- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 71 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, 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 and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- Ideal.mapstatement · cited by 692
- Ideal.subset_spanproof · cited by 86
Cited by71
Results whose statement or proof uses this declaration.
- Ideal.map_spanproof · cited by 43
- Ideal.mem_map_iff_of_surjectiveproof · cited by 19
- Ideal.map_comap_of_surjectiveproof · cited by 13
- IsLocalization.map_underproof · cited by 12
- Ideal.map_isPrime_of_surjectiveproof · cited by 11
- Ideal.map_mulproof · cited by 9
- Ideal.mem_map_C_iffproof · cited by 6
- IsLocalization.AtPrime.isUnit_to_map_iffproof · cited by 4
- Algebra.Generators.map_toComp_kerproof · cited by 3
- Ideal.lift_spanRank_map_leproof · cited by 3
- Ideal.map_includeRight_eqproof · cited by 3
- Ideal.spanIntNorm_localizationproof · cited by 3