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Theorems · Definition · logic and foundations

FirstOrder.Language.ElementarySubstructure.recOn

{L : FirstOrder.Language} →
  {M : Type u_1} →
    [inst : L.Structure M] →
      {motive : L.ElementarySubstructure M → Sort u} →
        (t : L.ElementarySubstructure M) →
          ((toSubstructure : L.Substructure M) →
              (isElementary' : toSubstructure.IsElementary) →
                motive { toSubstructure := toSubstructure, isElementary' := isElementary' }) →
            motive t
Defined in
Mathlib.ModelTheory.ElementarySubstructures
Cited by
0 results in Mathlib
Foundations
Depth 25 from the axioms · uses Quot.sound
Assumes
FirstOrder.Language.Structure
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FirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Substructure · cited by 242Language.SubstructureFirstOrder.Language.ElementarySubstructure · cited by 18Language.ElementarySubstr…FirstOrder.Language.Substructure.IsElementary · cited by 8Substructure.IsElementaryElementarySubstructure.recOnCITED BYCITES

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