Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.IsOrdered.leSymb

{L : FirstOrder.Language} → [self : L.IsOrdered] → L.Relations 2

The relation symbol representing ≤.

Defined in
Mathlib.ModelTheory.Order
Cited by
6 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
FirstOrder.Language.IsOrdered
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FirstOrder.Language.linearOrderTheory · cited by 7Language.linearOrderTheoryFirstOrder.Language.orderLHom · cited by 5Language.orderLHomFirstOrder.Language.linearOrderOfModels · cited by 2Language.linearOrderOfMod…FirstOrder.Language.HomClass.monotone · cited by 1HomClass.monotoneFirstOrder.Language.Term.le · cited by 1Term.leFirstOrder.Language.partialOrderTheory · cited by 0Language.partialOrderTheo…FirstOrder.Language.order.relation_eq_leSymb · cited by 0order.relation_eq_leSymbFirstOrder.Language.preorderTheory · cited by 0Language.preorderTheoryFirstOrder.Language.decidableLEOfStructure · cited by 0Language.decidableLEOfStr…FirstOrder.Language.leOfStructure · cited by 0Language.leOfStructureFirstOrder.Language.StrongHomClass.toOrderIsoClass · cited by 0StrongHomClass.toOrderIso…FirstOrder.Language.OrderedStructure.casesOn · cited by 0OrderedStructure.casesOnFirstOrder.Language.OrderedStructure.recOn · cited by 0OrderedStructure.recOnFirstOrder.Language.OrderedStructure.relMap_leSymb · cited by 0OrderedStructure.relMap_l…FirstOrder.Language.orderLHom_leSymb · cited by 0Language.orderLHom_leSymbFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Relations · cited by 147Language.RelationsFirstOrder.Language.IsOrdered · cited by 19Language.IsOrderedIsOrdered.leSymbCITED BYCITES

Cites3

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

Cited by16

Results whose statement or proof uses this declaration.