Theorems · Definition · logic and foundations
FirstOrder.Language.BoundedFormula.liftAt
{L : FirstOrder.Language} → {α : Type u'} → {n : ℕ} → (n' : ℕ) → ℕ → L.BoundedFormula α n → L.BoundedFormula α (n + n')Raises all of the bound variables of a formula greater than or equal to m by n'.
- Defined in
- Mathlib.ModelTheory.Syntax
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.BoundedFormulastatement and proof · cited by 207
- FirstOrder.Language.Termproof · cited by 166
- FirstOrder.Language.BoundedFormula.castLEproof · cited by 13
- FirstOrder.Language.BoundedFormula.mapTermRelproof · cited by 10
- FirstOrder.Language.Term.liftAtproof · cited by 3
Cited by14
Results whose statement or proof uses this declaration.
- FirstOrder.Language.BoundedFormula.IsQF.liftAtstatement and proof · cited by 3
- FirstOrder.Language.BoundedFormula.IsPrenex.liftAtstatement and proof · cited by 2
- FirstOrder.Language.BoundedFormula.realize_liftAt_onestatement · cited by 1
- FirstOrder.Language.BoundedFormula.IsAtomic.liftAtstatement · cited by 1
- FirstOrder.Language.BoundedFormula.toPrenexImp.eq_defstatement and proof · cited by 1
- FirstOrder.Language.BoundedFormula.toPrenexImpRight.eq_defstatement and proof · cited by 1
- FirstOrder.Language.BoundedFormula.realize_all_liftAt_one_selfstatement · cited by 1
- FirstOrder.Language.BoundedFormula.realize_toPrenexImpproof · cited by 1
- FirstOrder.Language.BoundedFormula.realize_toPrenexImpRightproof · cited by 1
- FirstOrder.Language.BoundedFormula.isPrenex_toPrenexImpproof · cited by 1
- FirstOrder.Language.BoundedFormula.isPrenex_toPrenexImpRightproof · cited by 1
- FirstOrder.Language.BoundedFormula.realize_liftAtstatement · cited by 0