Theorems · Theorem · logic and foundations

FirstOrder.Language.PartialEquiv.le_def

∀ {L : FirstOrder.Language} {M : Type w} {N : Type w'} [inst : L.Structure M] [inst_1 : L.Structure N]
  (f g : L.PartialEquiv M N),
  f ≤ g ↔
    ∃ (h : f.dom ≤ g.dom),
      g.cod.subtype.comp (g.toEquiv.toEmbedding.comp (FirstOrder.Language.Substructure.inclusion h)) =
        f.cod.subtype.comp f.toEquiv.toEmbedding

Defined in

Mathlib.ModelTheory.PartialEquiv

Cited by

2 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

FirstOrder.Language.StructureFirstOrder.Language.Structure