Theorems · Definition · logic and foundations

FirstOrder.Language.DirectLimit.unify

{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)) →
            {α : Type u_1} →
              (x : α → FirstOrder.Language.Structure.Sigma f) →
                (i : ι) → i ∈ upperBounds (Set.range (Sigma.fst ∘ x)) → α → G i

Raises a family of elements in the Σ-type to the same level along the embeddings.

Defined in

Mathlib.ModelTheory.DirectLimit

Cited by

10 results in Mathlib

Foundations

Depth 14 from the axioms · uses Quot.sound

Assumes

PreorderFirstOrder.Language.Structure