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Theorems · Theorem · order theory

SetLike.coe_set_eq

∀ {A : Type u_1} {B : Type u_2} [i : SetLike A B] {p q : A}, ↑p = ↑q ↔ p = q
Defined in
Mathlib.Data.SetLike.Basic
Cited by
27 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
SetLike
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SetLike.ext'_iff · cited by 78SetLike.ext'_iffFinset.coe_inj · cited by 41Finset.coe_injIdeal.map_includeRight_eq · cited by 3Ideal.map_includeRight_eqSublattice.coe_inj · cited by 3Sublattice.coe_injLieSubalgebra.coe_set_eq · cited by 2LieSubalgebra.coe_set_eqLowerSet.sdiff_eq_left · cited by 2LowerSet.sdiff_eq_leftLieRinehartSubalgebra.coe_set_eq · cited by 2LieRinehartSubalgebra.coe…ArchimedeanClass.addSubgroup_strictAntiOn · cited by 1ArchimedeanClass.addSubgr…Ideal.map_includeLeft_eq · cited by 1Ideal.map_includeLeft_eqBooleanSubalgebra.coe_inj · cited by 1BooleanSubalgebra.coe_injSubmodule.dense_iff_topologicalClosure_eq_top · cited by 1Submodule.dense_iff_topol…ArchimedeanClass.subsemigroup_strictAnti · cited by 1ArchimedeanClass.subsemig…LieSubmodule.isCompactElement_lieSpan_singleton · cited by 0LieSubmodule.isCompactEle…Finset.neg_product · cited by 0Finset.neg_productSubmodule.coe_eq_univ · cited by 0Submodule.coe_eq_univSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeSetLike · cited by 1084SetLikeSetLike.coe_injective · cited by 374SetLike.coe_injectiveSetLike.coe_set_eqCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by27

Results whose statement or proof uses this declaration.