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Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.map_iSup

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N] {ι : Sort u_3}
  (f : L.Hom M N) (s : ι → L.Substructure M),
  FirstOrder.Language.Substructure.map f (⨆ i, s i) = ⨆ i, FirstOrder.Language.Substructure.map f (s i)
Defined in
Mathlib.ModelTheory.Substructures
Cited by
1 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Structure
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FirstOrder.Language.DirectLimit.range_lift · cited by 1DirectLimit.range_liftiSup · cited by 2415iSupFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Substructure · cited by 242Language.SubstructureFirstOrder.Language.Hom · cited by 107Language.HomGaloisConnection.l_iSup · cited by 78GaloisConnection.l_iSupFirstOrder.Language.Substructure.map · cited by 49Substructure.mapFirstOrder.Language.Substructure.gc_map_comap · cited by 14Substructure.gc_map_comapSubstructure.map_iSupCITED BYCITES

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