Theorems · Theorem · logic and foundations
FirstOrder.Language.realize_denselyOrdered_iff
∀ {L : FirstOrder.Language} {M : Type w'} [inst : L.IsOrdered] [inst_1 : L.Structure M] [inst_2 : Preorder M]
[L.OrderedStructure M], M ⊨ L.denselyOrderedSentence ↔ DenselyOrdered M- Defined in
- Mathlib.ModelTheory.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- DenselyOrderedstatement and proof · cited by 471
- Fin.snocproof · cited by 113
- exists_betweenproof · cited by 102
- FirstOrder.Language.Term.realizeproof · cited by 81
- FirstOrder.Language.Sentence.Realizestatement · cited by 62
- FirstOrder.Language.IsOrderedstatement and proof · cited by 19
- FirstOrder.Language.OrderedStructurestatement and proof · cited by 16
- FirstOrder.Language.denselyOrderedSentencestatement · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Language.denselyOrdered_of_dloproof · cited by 1
- FirstOrder.Language.realize_denselyOrderedproof · cited by 0