Card \(\mathrm{Card}\) — Cardinal Class Predicate (Card, AST Constructor: TpCard)
Unary predicate Card(K) ⟷ ∃(C:Class)(|C| = K) asserting that K is the cardinality of some class (Entry ThmOmegaInOrdinals (3.63)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
Card
\(\mathrm{Card}\)
|
| Category | Predicate Symbol (Unary Class Predicate) |
| SML AST Constructor | HP (TpCard of 'Class_EXP) [in datatype Truth_p, typetheory.ML:671] |
| Constructor Arguments | 1. Class K : Class |
| Metatype / Signature | Class → Bool |
| Binder Status | No — Unary Predicate Symbol (Cardinal Class) |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathrm{Card} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | Card(K) ⟷ ∃(C:Class)(|C| = K) |
| Related Symbols & Kernel Entries |