Theorems · Definition · logic and foundations
FirstOrder.Language.Theory.Imp
{L : FirstOrder.Language} → {α : Type w} → {n : ℕ} → L.Theory → L.BoundedFormula α n → L.BoundedFormula α n → Propφ ⟹[T] ψ indicates that φ implies ψ in models of T.
- Defined in
- Mathlib.ModelTheory.Equivalence
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses no axioms
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.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.BoundedFormulastatement and proof · cited by 207
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.Theory.ModelsBoundedFormulaproof · cited by 30
Cited by16
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.iff_iff_imp_and_impstatement · cited by 3
- FirstOrder.Language.Theory.Imp.transstatement and proof · cited by 2
- FirstOrder.Language.Theory.imp_infstatement and proof · cited by 1
- FirstOrder.Language.Theory.imp_sup_leftstatement · cited by 1
- FirstOrder.Language.Theory.imp_sup_rightstatement · cited by 1
- FirstOrder.Language.Theory.inf_imp_leftstatement · cited by 1
- FirstOrder.Language.Theory.inf_imp_rightstatement · cited by 1
- FirstOrder.Language.Theory.sup_impstatement and proof · cited by 1
- FirstOrder.Language.Theory.imp_antisymmstatement and proof · cited by 0
- FirstOrder.Language.Theory.imp_inf_iffstatement and proof · cited by 0
- FirstOrder.Language.Theory.imp_topstatement · cited by 0
- FirstOrder.Language.Theory.sup_imp_iffstatement and proof · cited by 0