Theorems · Theorem · logic and foundations

FirstOrder.Language.DirectLimit.funMap_unify_equiv

∀ {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)] {n : ℕ} (F : L.Functions n)
  (x : Fin n → FirstOrder.Language.Structure.Sigma f) (i j : ι) (hi : i ∈ upperBounds (Set.range (Sigma.fst ∘ x)))
  (hj : j ∈ upperBounds (Set.range (Sigma.fst ∘ x))),
  FirstOrder.Language.Structure.Sigma.mk f i
      (FirstOrder.Language.Structure.funMap F (FirstOrder.Language.DirectLimit.unify f x i hi)) ≈
    FirstOrder.Language.Structure.Sigma.mk f j
      (FirstOrder.Language.Structure.funMap F (FirstOrder.Language.DirectLimit.unify f x j hj))

Defined in

Mathlib.ModelTheory.DirectLimit

Cited by

1 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Quot.sound

Assumes

PreorderFirstOrder.Language.StructureIsDirectedOrderDirectedSystem