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Theorems · Theorem · logic and foundations

FirstOrder.Language.orderedStructure_iff

∀ {L : FirstOrder.Language} {M : Type w'} [inst : L.IsOrdered] [inst_1 : L.Structure M] [inst_2 : LE M]
  [inst_3 : FirstOrder.Language.order.Structure M] [FirstOrder.Language.order.OrderedStructure M],
  L.OrderedStructure M ↔ L.orderLHom.IsExpansionOn M
Defined in
Mathlib.ModelTheory.Order
Cited by
0 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.IsOrderedFirstOrder.Language.StructureLEFirstOrder.Language.StructureFirstOrder.Language.OrderedStructure
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FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.LHom.IsExpansionOn · cited by 31LHom.IsExpansionOnFirstOrder.Language.IsOrdered · cited by 19Language.IsOrderedFirstOrder.Language.OrderedStructure · cited by 16Language.OrderedStructureFirstOrder.Language.order · cited by 14Language.orderFirstOrder.Language.orderLHom · cited by 5Language.orderLHomLanguage.orderedStructure_iffCITED BYCITES

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