Documentation

Arithmetization.ISigmaOne.Metamath.Proof.Thy

Instances For
    structure LO.Arith.Language.Theory {V : Type u_1} [LO.ORingStruc V] (L : LO.Arith.Language V) {pL : LO.FirstOrder.Arith.LDef} [L.Defined pL] :
    Type u_1
    Instances For
      instance LO.Arith.instMembershipTheory {V : Type u_1} [LO.ORingStruc V] (L : LO.Arith.Language V) {pL : LO.FirstOrder.Arith.LDef} [L.Defined pL] :
      Membership V L.Theory
      Equations
      instance LO.Arith.instHasSubsetTheory {V : Type u_1} [LO.ORingStruc V] (L : LO.Arith.Language V) {pL : LO.FirstOrder.Arith.LDef} [L.Defined pL] :
      HasSubset L.Theory
      Equations
      theorem LO.Arith.Language.Theory.mem_def {V : Type u_1} [LO.ORingStruc V] (L : LO.Arith.Language V) {pL : LO.FirstOrder.Arith.LDef} [L.Defined pL] {T : L.Theory} {p : V} :
      p T p T.set
      class LO.Arith.Language.Theory.Defined {V : Type u_1} [LO.ORingStruc V] {L : LO.Arith.Language V} {pL : LO.FirstOrder.Arith.LDef} [L.Defined pL] (T : L.Theory) (pT : outParam pL.TDef) :
      Instances
        theorem LO.Arith.Language.Theory.Defined.defined {V : Type u_1} [LO.ORingStruc V] {L : LO.Arith.Language V} {pL : LO.FirstOrder.Arith.LDef} [L.Defined pL] {T : L.Theory} {pT : outParam pL.TDef} [self : T.Defined pT] :
        𝚫₁-Predicate fun (x : V) => x T.set via pT.ch
        instance LO.Arith.Language.Theory.mem_definable {V : Type u_1} [LO.ORingStruc V] {L : LO.Arith.Language V} {pL : LO.FirstOrder.Arith.LDef} [L.Defined pL] (T : L.Theory) {pT : pL.TDef} [T.Defined pT] :
        𝚫₁-Predicate fun (x : V) => x T
        Equations
        • =