Mathlib Map

Theorems · Theorem · logic and foundations

FirstOrder.Language.LHom.map_onFunction

∀ {L : FirstOrder.Language} {L' : FirstOrder.Language} (ϕ : L →ᴸ L') {M : Type u_1} [inst : L.Structure M]
  [inst_1 : L'.Structure M] [ϕ.IsExpansionOn M] {n : ℕ} (f : L.Functions n) (x : Fin n → M),
  FirstOrder.Language.Structure.funMap (ϕ.onFunction f) x = FirstOrder.Language.Structure.funMap f x
Defined in
Mathlib.ModelTheory.LanguageMap
Cited by
5 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
FirstOrder.Language.StructureFirstOrder.Language.StructureFirstOrder.Language.LHom.IsExpansionOn
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FirstOrder.Language.withConstants_funMap_sumInl · cited by 3Language.withConstants_fu…FirstOrder.Language.LHom.realize_onTerm · cited by 3LHom.realize_onTermFirstOrder.Language.withConstants_funMap_sumInr · cited by 1Language.withConstants_fu…FirstOrder.Language.LHom.funMap_sumInl · cited by 0LHom.funMap_sumInlFirstOrder.Language.LHom.funMap_sumInr · cited by 0LHom.funMap_sumInrFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Functions · cited by 153Language.FunctionsFirstOrder.Language.Structure.funMap · cited by 69Structure.funMapFirstOrder.Language.LHom · cited by 66Language.LHomFirstOrder.Language.LHom.IsExpansionOn · cited by 31LHom.IsExpansionOnFirstOrder.Language.LHom.onFunction · cited by 27LHom.onFunctionFirstOrder.Language.LHom.IsExpansionOn.map_onFunction · cited by 1IsExpansionOn.map_onFunct…LHom.map_onFunctionCITED BYCITES

Cites8

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

Cited by5

Results whose statement or proof uses this declaration.