Tight \(\mathrm{Tight}\) — Replacement-Closed Class Predicate (Tight, AST Constructor: TpTight)
Unary predicate Tight(U) asserting closure of U under images of class-functions (Entry DefTightClass (3.47)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
Tight
\(\mathrm{Tight}\)
|
| Category | Predicate Symbol (Unary Class Predicate) |
| SML AST Constructor | HP (TpTight of 'Class_EXP) [in datatype Truth_p, typetheory.ML:668] |
| 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{Tight} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | Tight(U) ⟷ ∀(f:Class)((f is a class-function) → ∀(x∈U)((x⊆Dom(f)) → (f[x]∈U))) |
| Related Symbols & Kernel Entries |