Mathlib Map

Theorems · Theorem · logic and foundations

FirstOrder.Language.Theory.IsMaximal.isComplete

∀ {L : FirstOrder.Language} {T : L.Theory}, T.IsMaximal → T.IsComplete
Defined in
Mathlib.ModelTheory.Satisfiability
Cited by
2 results in Mathlib
Foundations
Depth 26 from the axioms · uses Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FirstOrder.Language.completeTheory.isComplete · cited by 0completeTheory.isCompleteFirstOrder.Language.Theory.exists_modelType_is_realized_in · cited by 0Theory.exists_modelType_i…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.Theory.IsComplete · cited by 11Theory.IsCompleteFirstOrder.Language.Theory.IsMaximal · cited by 10Theory.IsMaximalFirstOrder.Language.Theory.models_sentence_of_mem · cited by 3Theory.models_sentence_of…IsMaximal.isCompleteCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.