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Theorems · Definition · logic and foundations

FirstOrder.Language.preorderOfModels

(L : FirstOrder.Language) →
  (M : Type w') → [inst : L.IsOrdered] → [inst_1 : L.Structure M] → [h : M ⊨ L.preorderTheory] → Preorder M

Any model of a theory of preorders is a preorder.

Defined in
Mathlib.ModelTheory.Order
Cited by
0 results in Mathlib
Foundations
Depth 37 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.IsOrderedFirstOrder.Language.StructureFirstOrder.Language.Theory.Model
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FirstOrder.Language.partialOrderOfModels · cited by 0Language.partialOrderOfMo…Preorder · cited by 7952PreorderFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Theory.Model · cited by 67Theory.ModelFirstOrder.Language.IsOrdered · cited by 19Language.IsOrderedFirstOrder.Language.preorderTheory · cited by 0Language.preorderTheoryFirstOrder.Language.leOfStructure · cited by 0Language.leOfStructureLanguage.preorderOfModelsCITED BYCITES

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