Theorems · Theorem · logic and foundations

FirstOrder.Language.DirectLimit.relMap_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)) [IsDirectedOrder ι] [DirectedSystem G fun i j h => ⇑(f i j h)]
  {n : ℕ} (R : L.Relations 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.RelMap R (FirstOrder.Language.DirectLimit.unify f x i hi) =
    FirstOrder.Language.Structure.RelMap R (FirstOrder.Language.DirectLimit.unify f x j hj)

Defined in

Mathlib.ModelTheory.DirectLimit

Cited by

1 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

PreorderFirstOrder.Language.StructureIsDirectedOrderDirectedSystem