Theorems · Theorem · logic and foundations

FirstOrder.Language.DirectLimit.equiv_iff

∀ {L : FirstOrder.Language} {ι : Type v} [inst : Preorder ι] (G : ι → Type w) [inst_1 : (i : ι) → L.Structure (G i)]
  (f : (i j : ι) → i ≤ j → L.Embedding (G i) (G j)) [inst_2 : IsDirectedOrder ι]
  [inst_3 : DirectedSystem G fun i j h => ⇑(f i j h)] {x y : FirstOrder.Language.Structure.Sigma f} {i : ι}
  (hx : x.fst ≤ i) (hy : y.fst ≤ i), x ≈ y ↔ (f x.fst i hx) x.snd = (f y.fst i hy) y.snd

Defined in

Mathlib.ModelTheory.DirectLimit

Cited by

3 results in Mathlib

Foundations

Depth 17 from the axioms · uses Quot.sound

Assumes

PreorderFirstOrder.Language.StructureIsDirectedOrderDirectedSystem