Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.PartialEquiv.toEquiv

{L : FirstOrder.Language} →
  {M : Type w} →
    {N : Type w'} →
      [inst : L.Structure M] → [inst_1 : L.Structure N] → (self : L.PartialEquiv M N) → L.Equiv ↥self.dom ↥self.cod

The equivalence between the two subdomains.

Defined in
Mathlib.ModelTheory.PartialEquiv
Cited by
24 results in Mathlib
Foundations
Depth 18 from the axioms · uses no axioms
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Structure

Around this declaration

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

FirstOrder.Language.PartialEquiv.symm · cited by 9PartialEquiv.symmFirstOrder.Language.PartialEquiv.dom_le_dom · cited by 8PartialEquiv.dom_le_domFirstOrder.Language.DirectLimit.partialEquivLimit · cited by 6DirectLimit.partialEquivL…FirstOrder.Language.PartialEquiv.cod_le_cod · cited by 6PartialEquiv.cod_le_codFirstOrder.Language.PartialEquiv.ext · cited by 3PartialEquiv.extFirstOrder.Language.PartialEquiv.subtype_toEquiv_inclusion · cited by 3PartialEquiv.subtype_toEq…FirstOrder.Language.PartialEquiv.le_def · cited by 2PartialEquiv.le_defFirstOrder.Language.Embedding.toPartialEquiv_toEmbedding · cited by 2Embedding.toPartialEquiv_…FirstOrder.Language.PartialEquiv.toEmbedding · cited by 2PartialEquiv.toEmbeddingFirstOrder.Language.PartialEquiv.toEquivOfEqTop · cited by 2PartialEquiv.toEquivOfEqT…FirstOrder.Language.PartialEquiv.toEquiv_inclusion_apply · cited by 2PartialEquiv.toEquiv_incl…FirstOrder.Language.DirectLimit.le_partialEquivLimit · cited by 2DirectLimit.le_partialEqu…FirstOrder.Language.PartialEquiv.domRestrict · cited by 2PartialEquiv.domRestrictFirstOrder.Language.PartialEquiv.ext_iff · cited by 1PartialEquiv.ext_iffFirstOrder.Language.PartialEquiv.le_domRestrict · cited by 1PartialEquiv.le_domRestri…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Substructure · cited by 242Language.SubstructureFirstOrder.Language.Equiv · cited by 83Language.EquivFirstOrder.Language.PartialEquiv · cited by 44Language.PartialEquivFirstOrder.Language.PartialEquiv.dom · cited by 35PartialEquiv.domFirstOrder.Language.PartialEquiv.cod · cited by 32PartialEquiv.codPartialEquiv.toEquivCITED BYCITES

Cites7

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Cited by29

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