Theorems · Definition · logic and foundations

FirstOrder.Language.Theory.IsUniversal.casesOn

{L : FirstOrder.Language} →
  {T : L.Theory} →
    {motive : T.IsUniversal → Sort u_1} →
      (t : T.IsUniversal) →
        ((isUniversal_of_mem : ∀ ⦃φ : L.Sentence⦄, φ ∈ T → FirstOrder.Language.BoundedFormula.IsUniversal φ) →
            motive ⋯) →
          motive t

Defined in: Mathlib.ModelTheory.Complexity
Cited by: 0 results in Mathlib
Foundations: Depth 10 from the axioms · uses no axioms

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

FirstOrder.Languagestatement and proof · cited by 1,084
FirstOrder.Language.Theorystatement and proof · cited by 154
FirstOrder.Language.Sentencestatement and proof · cited by 127
FirstOrder.Language.BoundedFormula.IsUniversalstatement and proof · cited by 12
FirstOrder.Language.Theory.IsUniversalstatement and proof · cited by 3

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.