Theorems · Theorem · logic and foundations

FirstOrder.Language.DirectLimit.unify_sigma_mk_self

∀ {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)) [DirectedSystem G fun i j h => ⇑(f i j h)] {α : Type u_1} {i : ι}
  {x : α → G i},
  FirstOrder.Language.DirectLimit.unify f (fun a => FirstOrder.Language.Structure.Sigma.mk f i (x a)) i ⋯ = x

Defined in

Mathlib.ModelTheory.DirectLimit

Cited by

1 results in Mathlib

Foundations

Depth 16 from the axioms · uses Quot.sound

Assumes

PreorderFirstOrder.Language.StructureDirectedSystem