- ch : 𝚫₁.Semisentence 1
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
- set : Set V
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
- LO.Arith.instMembershipTheory L = { mem := fun (x : V) (T : L.Theory) => x ∈ T.set }
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
- LO.Arith.instHasSubsetTheory L = { Subset := fun (T U : L.Theory) => T.set ⊆ U.set }
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}
:
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)
:
- defined : 𝚫₁-Predicate fun (x : V) => x ∈ T.set via pT.ch
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
- ⋯ = ⋯