Theorems · Definition · logic and foundations
FirstOrder.Language.BoundedFormula.freeVarFinset
{L : FirstOrder.Language} → {α : Type u'} → [DecidableEq α] → {n : ℕ} → L.BoundedFormula α n → Finset αThe Finset of free variables used in a given formula.
- Defined in
- Mathlib.ModelTheory.Syntax
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.BoundedFormulastatement and proof · cited by 207
- FirstOrder.Language.BoundedFormula.brecOnproof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- FirstOrder.Language.BoundedFormula.restrictFreeVarstatement and proof · cited by 7
- FirstOrder.Language.BoundedFormula.realize_restrictFreeVarstatement and proof · cited by 4
- FirstOrder.Language.Formula.exClosureproof · cited by 4
- FirstOrder.Language.ElementaryEmbedding.map_boundedFormulaproof · cited by 2
- FirstOrder.Language.Formula.realize_exClosurestatement and proof · cited by 2
- FirstOrder.Language.BoundedFormula.realize_restrictFreeVar'statement and proof · cited by 1
- Set.definable_iff_finitely_definableproof · cited by 1
- FirstOrder.Language.BoundedFormula.restrictFreeVar.eq_defstatement and proof · cited by 0
- FirstOrder.Language.BoundedFormula.freeVarFinset.eq_defstatement and proof · cited by 0
- FirstOrder.Language.Formula.realize_exClosure_of_realize_equivSentenceproof · cited by 0