Theorems · Theorem · order theory
SetLike.coe_injective
∀ {A : Type u_1} {B : outParam (Type u_2)} [self : SetLike A B], Function.Injective SetLike.coeThe coercion from a term of a SetLike to its corresponding Set is injective.
- Defined in
- Mathlib.Data.SetLike.Basic
- Cited by
- 374 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 6 definitions · uses no axioms
- Assumes
- SetLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- SetLikestatement and proof · cited by 1,084
Cited by375
Results whose statement or proof uses this declaration.
- SetLike.extproof · cited by 92
- TopologicalSpace.Opens.extproof · cited by 83
- SetLike.ext_iffproof · cited by 64
- SetLike.ext'proof · cited by 60
- LinearMap.range_compproof · cited by 52
- Subgroup.range_subtypeproof · cited by 28
- Algebra.map_topproof · cited by 27
- SetLike.coe_set_eqproof · cited by 27
- Submodule.restrictScalars_selfproof · cited by 20
- Submodule.map_compproof · cited by 19
- AddSubgroup.range_subtypeproof · cited by 16
- TopologicalSpace.Compacts.isEmbedding_coeproof · cited by 10
Showing the 200 most cited of 375.