Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.comap_map_comap

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N]
  {S : L.Substructure N} {f : L.Hom M N},
  FirstOrder.Language.Substructure.comap f
      (FirstOrder.Language.Substructure.map f (FirstOrder.Language.Substructure.comap f S)) =
    FirstOrder.Language.Substructure.comap f S

Defined in: Mathlib.ModelTheory.Substructures
Cited by: 0 results in Mathlib
Foundations: Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: FirstOrder.Language.Structure FirstOrder.Language.Structure

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FirstOrder.Languagestatement and proof · cited by 1,084
FirstOrder.Language.Structurestatement and proof · cited by 775
FirstOrder.Language.Substructurestatement and proof · cited by 242
FirstOrder.Language.Homstatement and proof · cited by 107
FirstOrder.Language.Substructure.mapstatement · cited by 49
FirstOrder.Language.Substructure.comapstatement · cited by 31
GaloisConnection.u_l_u_eq_uproof · cited by 17
FirstOrder.Language.Substructure.gc_map_comapproof · cited by 14

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