Mathlib Map

Theorems · Inductive type · logic and foundations

FirstOrder.Language.BoundedFormula.IsExistential

{L : FirstOrder.Language} → {α : Type u'} → {n : ℕ} → L.BoundedFormula α n → Prop

An existential formula is a formula defined by applying only existential quantifiers to a quantifier-free formula.

Defined in
Mathlib.ModelTheory.Complexity
Cited by
4 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
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FirstOrder.Language.BoundedFormula.IsQF.isExistential · cited by 1IsQF.isExistentialFirstOrder.Language.BoundedFormula.IsExistential.below · cited by 1IsExistential.belowFirstOrder.Language.BoundedFormula.IsExistential.brecOn · cited by 0IsExistential.brecOnFirstOrder.Language.BoundedFormula.IsExistential.casesOn · cited by 0IsExistential.casesOnFirstOrder.Language.BoundedFormula.IsExistential.realize_embedding · cited by 0IsExistential.realize_emb…FirstOrder.Language.BoundedFormula.IsExistential.recOn · cited by 0IsExistential.recOnFirstOrder.Language.BoundedFormula.IsExistential.below.casesOn · cited by 0below.casesOnFirstOrder.Language.BoundedFormula.IsAtomic.isExistential · cited by 0IsAtomic.isExistentialFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.BoundedFormula · cited by 207Language.BoundedFormulaBoundedFormula.IsExistentialCITED BYCITES

Cites2

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

Cited by8

Results whose statement or proof uses this declaration.