Documentation

Arithmetization.ISigmaOne.Metamath.CodedTheory

def LO.FirstOrder.Theory.tDef {L : LO.FirstOrder.Language} [(k : ) → Encodable (L.Func k)] [(k : ) → Encodable (L.Rel k)] [LO.Arith.DefinableLanguage L] (T : LO.FirstOrder.Theory L) [d : T.Delta1Definable] :
L.lDef.TDef
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    def LO.FirstOrder.Theory.codeIn {L : LO.FirstOrder.Language} [(k : ) → Encodable (L.Func k)] [(k : ) → Encodable (L.Rel k)] [LO.Arith.DefinableLanguage L] (V : Type u_1) [LO.ORingStruc V] (T : LO.FirstOrder.Theory L) [T.Delta1Definable] :
    (L.codeIn V).Theory
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      instance LO.Arith.tDef_defined {L : LO.FirstOrder.Language} [(k : ) → Encodable (L.Func k)] [(k : ) → Encodable (L.Rel k)] [LO.Arith.DefinableLanguage L] {V : Type u_1} [LO.ORingStruc V] [V ⊧ₘ* 𝐈𝚺₁] {T : LO.FirstOrder.Theory L} [T.Delta1Definable] :
      (LO.FirstOrder.Theory.codeIn V T).Defined T.tDef
      Equations
      • LO.Arith.tDef_defined = { defined := }
      def LO.FirstOrder.Theory.tCodeIn {L : LO.FirstOrder.Language} [(k : ) → Encodable (L.Func k)] [(k : ) → Encodable (L.Rel k)] [LO.Arith.DefinableLanguage L] (V : Type u_1) [LO.ORingStruc V] [V ⊧ₘ* 𝐈𝚺₁] (T : LO.FirstOrder.Theory L) [T.Delta1Definable] :
      (L.codeIn V).TTheory
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        def LO.FirstOrder.Theory.Delta1Definable.add {L : LO.FirstOrder.Language} [(k : ) → Encodable (L.Func k)] [(k : ) → Encodable (L.Rel k)] [LO.Arith.DefinableLanguage L] {T : LO.FirstOrder.Theory L} {U : LO.FirstOrder.Theory L} (dT : T.Delta1Definable) (dU : U.Delta1Definable) :
        (T + U).Delta1Definable
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          def LO.FirstOrder.Theory.Delta1Definable.ofEq {L : LO.FirstOrder.Language} [(k : ) → Encodable (L.Func k)] [(k : ) → Encodable (L.Rel k)] [LO.Arith.DefinableLanguage L] {T : LO.FirstOrder.Theory L} {U : LO.FirstOrder.Theory L} (dT : T.Delta1Definable) (h : T = U) :
          U.Delta1Definable
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            def LO.FirstOrder.Theory.Delta1Definable.add_subset_left {L : LO.FirstOrder.Language} [(k : ) → Encodable (L.Func k)] [(k : ) → Encodable (L.Rel k)] [LO.Arith.DefinableLanguage L] {V : Type u_1} [LO.ORingStruc V] {T : LO.FirstOrder.Theory L} {U : LO.FirstOrder.Theory L} (dT : T.Delta1Definable) (dU : U.Delta1Definable) :
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            • =
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              def LO.FirstOrder.Theory.Delta1Definable.add_subset_right {L : LO.FirstOrder.Language} [(k : ) → Encodable (L.Func k)] [(k : ) → Encodable (L.Rel k)] [LO.Arith.DefinableLanguage L] {V : Type u_1} [LO.ORingStruc V] {T : LO.FirstOrder.Theory L} {U : LO.FirstOrder.Theory L} (dT : T.Delta1Definable) (dU : U.Delta1Definable) :
              Equations
              • =
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