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Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.map_le_iff_le_comap

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N] {f : L.Hom M N}
  {S : L.Substructure M} {T : L.Substructure N},
  FirstOrder.Language.Substructure.map f S ≤ T ↔ S ≤ FirstOrder.Language.Substructure.comap f T
Defined in
Mathlib.ModelTheory.Substructures
Cited by
3 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Structure
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FirstOrder.Language.Substructure.gc_map_comap · cited by 14Substructure.gc_map_comapFirstOrder.Language.Substructure.map_closure · cited by 4Substructure.map_closureFirstOrder.Language.Hom.range_le_iff_comap · cited by 0Hom.range_le_iff_comapFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Substructure · cited by 242Language.SubstructureSet.image_subset_iff · cited by 203Set.image_subset_iffFirstOrder.Language.Hom · cited by 107Language.HomFirstOrder.Language.Substructure.map · cited by 49Substructure.mapFirstOrder.Language.Substructure.comap · cited by 31Substructure.comapSubstructure.map_le_iff_le_co…CITED BYCITES

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Cited by3

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