Mathlib Map

Theorems · Theorem · logic and foundations

FirstOrder.Language.ElementarilyEquivalent.theory_model

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N] {T : L.Theory}
  [MT : M ⊨ T], L.ElementarilyEquivalent M N → N ⊨ T
Defined in
Mathlib.ModelTheory.Semantics
Cited by
1 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.StructureFirstOrder.Language.Theory.Model
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FirstOrder.Language.Theory.exists_model_card_eq · cited by 1Theory.exists_model_card_…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Theory.Model · cited by 67Theory.ModelFirstOrder.Language.ElementarilyEquivalent · cited by 19Language.ElementarilyEqui…FirstOrder.Language.ElementarilyEquivalent.theory_model_iff · cited by 3ElementarilyEquivalent.th…ElementarilyEquivalent.theory…CITED BYCITES

Cites6

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

Cited by1

Results whose statement or proof uses this declaration.