Theorems · Theorem · logic and foundations

FirstOrder.Language.DirectLimit.rangeLiftInclusion

∀ {L : FirstOrder.Language} {ι : Type v} [inst : Preorder ι] [inst_1 : Nonempty ι] [inst_2 : IsDirectedOrder ι]
  {M : Type u_1} [inst_3 : L.Structure M] (S : ι →o L.Substructure M),
  (FirstOrder.Language.DirectLimit.liftInclusion S).toHom.range = ⨆ i, S i

Defined in

Mathlib.ModelTheory.DirectLimit

Cited by

0 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderNonemptyIsDirectedOrderFirstOrder.Language.Structure