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Theorems · Definition · order theory

Set.inclusion

{α : Type u_1} → {s t : Set α} → s ⊆ t → ↑s → ↑t

inclusion is the "identity" function between two subsets s and t, where s ⊆ t

Defined in
Mathlib.Data.Set.Inclusion
Cited by
145 results in Mathlib
Foundations
Depth 7 from the axioms, rests on 14 definitions · uses no axioms
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Around this declaration

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

AffineSubspace.inclusion · cited by 39AffineSubspace.inclusionSubalgebra.inclusion · cited by 36Subalgebra.inclusionAffine.Simplex.restrict · cited by 35Simplex.restrictSet.inclusion_injective · cited by 28Set.inclusion_injectiveLinearIndepOn.mono · cited by 14LinearIndepOn.monocfcₙ_eq_cfc · cited by 13cfcₙ_eq_cfcNonUnitalSubalgebra.inclusion · cited by 12NonUnitalSubalgebra.inclu…Set.range_inclusion · cited by 12Set.range_inclusioncontinuous_inclusion · cited by 8continuous_inclusionTopology.IsEmbedding.inclusion · cited by 8IsEmbedding.inclusioncfcₙHom_of_cfcHom · cited by 6cfcₙHom_of_cfcHomSet.coe_inclusion · cited by 6Set.coe_inclusionFirstOrder.Language.PartialEquiv.cod_le_cod · cited by 6PartialEquiv.cod_le_codSet.card_le_card · cited by 5Set.card_le_cardSublattice.inclusion · cited by 5Sublattice.inclusionSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemSet.inclusionCITED BYCITES

Cites2

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

  • Setstatement and proof · cited by 53,352
  • Set.Elemstatement and proof · cited by 7,166

Cited by160

Results whose statement or proof uses this declaration.