Theorems · Definition · logic and foundations
FirstOrder.Language.BoundedFormula.iInf
{L : FirstOrder.Language} →
{α : Type u'} → {β : Type v'} → {n : ℕ} → [Finite β] → (β → L.BoundedFormula α n) → L.BoundedFormula α nTake the conjunction of a finite set of formulas. Note that this is an arbitrary formula defined using the axiom of choice. It is only well-defined up to equivalence of formulas.
- Defined in
- Mathlib.ModelTheory.Syntax
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Fintypeproof · cited by 7,736
- Finset.univproof · cited by 3,473
- Finitestatement and proof · cited by 3,029
- FirstOrder.Languagestatement and proof · cited by 1,084
- Fintype.ofFiniteproof · cited by 255
- FirstOrder.Language.BoundedFormulastatement and proof · cited by 207
- Finset.toListproof · cited by 34
Cited by8
Results whose statement or proof uses this declaration.
- FirstOrder.genericPolyMapSurjOnOfInjOnproof · cited by 4
- FirstOrder.Language.Formula.iInfproof · cited by 3
- FirstOrder.Language.Formula.iExsUniqueproof · cited by 2
- FirstOrder.realize_genericPolyMapSurjOnOfInjOnproof · cited by 2
- FirstOrder.Ring.mvPolynomial_zeroLocus_definableproof · cited by 1
- FirstOrder.Language.Formula.realize_iExsUniqueproof · cited by 1
- FirstOrder.Language.BoundedFormula.iInf.congr_simpstatement and proof · cited by 1
- FirstOrder.Language.BoundedFormula.realize_iInfstatement · cited by 0