Powerful \(\mathrm{Powerful}\) — Power-Closed Class Predicate (Powerful, AST Constructor: TpPowerful)
Unary predicate Powerful(U) ⟷ ∀(x∈U)(𝒫(x) ∈ U) asserting closure under power sets (Entry DefPowerfulClass (3.45)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
Powerful
\(\mathrm{Powerful}\)
|
| Category | Predicate Symbol (Unary Class Predicate) |
| SML AST Constructor | HP (TpPowerful of 'Class_EXP) [in datatype Truth_p, typetheory.ML:666] |
| 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{Powerful} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | Powerful(U) ⟷ ∀(x∈U)(𝒫(x) ∈ U) |
| Related Symbols & Kernel Entries |