Pairful \(\mathrm{Pairful}\) — Pair-Closed Class Predicate (Pairful, AST Constructor: TpPairful)
Unary predicate Pairful(U) ⟷ ∀(x∈U)∀(y∈U)({x,y} ∈ U) asserting closure under unordered pairs (Entry DefPairfulClass (3.46)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
Pairful
\(\mathrm{Pairful}\)
|
| Category | Predicate Symbol (Unary Class Predicate) |
| SML AST Constructor | HP (TpPairful of 'Class_EXP) [in datatype Truth_p, typetheory.ML:667] |
| Constructor Arguments | 1. Class U : Class |
| Metatype / Signature | Class → Bool |
| Binder Status | No — Unary Predicate Symbol |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathrm{Pairful} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | Pairful(U) ⟷ ∀(x∈U)∀(y∈U)({x,y} ∈ U) |
| Related Symbols & Kernel Entries |