Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.con

(L : FirstOrder.Language) → {α : Type w'} → α → (L.withConstants α).Constants

The constant symbol indexed by a particular element.

Defined in
Mathlib.ModelTheory.LanguageMap
Cited by
21 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Language.distinctConstantsTheory · cited by 9Language.distinctConstant…FirstOrder.Language.Formula.realize_equivSentence_symm_con · cited by 4Formula.realize_equivSent…FirstOrder.Language.Term.realize_varsToConstants · cited by 3Term.realize_varsToConsta…FirstOrder.Language.model_distinctConstantsTheory · cited by 2Language.model_distinctCo…FirstOrder.Language.Formula.realize_equivSentence · cited by 2Formula.realize_equivSent…FirstOrder.Language.Term.realize_constantsToVars · cited by 1Term.realize_constantsToV…FirstOrder.Language.Term.realize_constantsVarsEquivLeft · cited by 1Term.realize_constantsVar…FirstOrder.Language.definableFun_const · cited by 1Language.definableFun_con…FirstOrder.Language.Theory.isSatisfiable_union_distinctConstantsTheory_of_card_le · cited by 1Theory.isSatisfiable_unio…FirstOrder.Language.distinctConstantsTheory_eq_iUnion · cited by 1Language.distinctConstant…FirstOrder.Language.Theory.models_formula_iff_onTheory_models_equivSentence · cited by 1Theory.models_formula_iff…FirstOrder.Language.withConstants_funMap_sumInr · cited by 1Language.withConstants_fu…FirstOrder.Language.BoundedFormula.realize_constantsVarsEquiv · cited by 1BoundedFormula.realize_co…Set.Definable.singleton · cited by 1Definable.singletonFirstOrder.Language.presburger.term_realize_eq_add_dotProduct · cited by 1presburger.term_realize_e…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.withConstants · cited by 108Language.withConstantsFirstOrder.Language.Constants · cited by 14Language.ConstantsLanguage.conCITED BYCITES

Cites3

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

Cited by22

Results whose statement or proof uses this declaration.