Theorems · Theorem · group theory
EmbeddingLike.map_eq_zero_iff
∀ {F : Type u_1} {M : Type u_4} {N : Type u_5} [inst : Zero M] [inst_1 : Zero N] [inst_2 : FunLike F M N]
[EmbeddingLike F M N] [ZeroHomClass F M N] {f : F} {x : M}, f x = 0 ↔ x = 0- Defined in
- Mathlib.Algebra.Group.Equiv.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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
- FunLikestatement and proof · cited by 2,560
- ZeroHomClassstatement and proof · cited by 74
- map_eq_zero_iffproof · cited by 62
- EmbeddingLikestatement and proof · cited by 20
- EmbeddingLike.injectiveproof · cited by 14
Cited by9
Results whose statement or proof uses this declaration.
- EmbeddingLike.map_ne_zero_iffproof · cited by 6
- AddEquiv.map_eq_zero_iffproof · cited by 6
- Algebra.Generators.Cotangent.exactproof · cited by 6
- AlgEquiv.eq_linearEquivConjAlgEquivproof · cited by 4
- MonomialOrder.eq_C_of_degree_eq_zeroproof · cited by 2
- Polynomial.comp_X_add_C_eq_zero_iffproof · cited by 1
- RingEquiv.map_eq_zero_iffproof · cited by 1
- AddEquivClass.map_eq_zero_iffproof · cited by 0
- IsDedekindDomain.HeightOneSpectrum.uniformContinuous_algebraMap_liesOverproof · cited by 0