Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.denselyOrderedSentence

(L : FirstOrder.Language) → [L.IsOrdered] → L.Sentence

A sentence indicating that an order is dense: $\forall x, \forall y, x < y \to \exists z, x < z \wedge z < y$.

Defined in
Mathlib.ModelTheory.Order
Cited by
5 results in Mathlib
Foundations
Depth 35 from the axioms · uses propext
Assumes
FirstOrder.Language.IsOrdered
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FirstOrder.Language.dlo · cited by 8Language.dloFirstOrder.Language.realize_denselyOrdered_iff · cited by 2Language.realize_denselyO…FirstOrder.Language.denselyOrdered_of_dlo · cited by 1Language.denselyOrdered_o…FirstOrder.Language.noBotOrder_of_dlo · cited by 1Language.noBotOrder_of_dloFirstOrder.Language.noTopOrder_of_dlo · cited by 1Language.noTopOrder_of_dloFirstOrder.Language.realize_denselyOrdered · cited by 0Language.realize_denselyO…FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Sentence · cited by 127Language.SentenceFirstOrder.Language.IsOrdered · cited by 19Language.IsOrderedFirstOrder.Language.BoundedFormula.ex · cited by 14BoundedFormula.exFirstOrder.Language.Term.lt · cited by 1Term.ltLanguage.denselyOrderedSenten…CITED BYCITES

Cites5

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

Cited by6

Results whose statement or proof uses this declaration.