Mathlib Map

Theorems · Theorem · logic and foundations

FirstOrder.Language.LHom.onTheory_model

∀ {L : FirstOrder.Language} {L' : FirstOrder.Language} {M : Type w} [inst : L.Structure M] [inst_1 : L'.Structure M]
  (φ : L →ᴸ L') [φ.IsExpansionOn M] (T : L.Theory), M ⊨ φ.onTheory T ↔ M ⊨ T
Defined in
Mathlib.ModelTheory.Semantics
Cited by
3 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
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.Theory.ModelsBoundedFormula.realize_formula · cited by 2ModelsBoundedFormula.real…FirstOrder.Language.Theory.isSatisfiable_union_distinctConstantsTheory_of_card_le · cited by 1Theory.isSatisfiable_unio…FirstOrder.Language.Theory.models_formula_iff_onTheory_models_equivSentence · cited by 1Theory.models_formula_iff…Set.image · cited by 5609Set.imageFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.Theory.Model · cited by 67Theory.ModelFirstOrder.Language.LHom · cited by 66Language.LHomFirstOrder.Language.Sentence.Realize · cited by 62Sentence.RealizeFirstOrder.Language.LHom.IsExpansionOn · cited by 31LHom.IsExpansionOnFirstOrder.Language.LHom.onTheory · cited by 27LHom.onTheoryFirstOrder.Language.LHom.onSentence · cited by 3LHom.onSentenceLHom.onTheory_modelCITED BYCITES

Cites11

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

Cited by3

Results whose statement or proof uses this declaration.