Tr \(\mathrm{Tr}\) — Transitive Class Predicate (Tr, AST Constructor: TpTrans)
Unary predicate Tr(X) asserting that every element of X is a subclass of X (Entry DefTransitiveClass (3.15)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
Tr
\(\mathrm{Tr}\)
|
| Category | Predicate Symbol (Unary Class Predicate) |
| SML AST Constructor | HP (TpTrans of 'Class_EXP) [in datatype Truth_p, typetheory.ML:664] |
| Constructor Arguments | 1. Class term X : Class |
| Metatype / Signature | Class → Bool |
| Binder Status | No — Defined Unary Predicate Symbol (Transitive Class) |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathrm{Tr} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | ∀(X:Class)(Tr(X) ⟷ (∀(y:Class)((y ∈ X) → (y ⊆ X)))) |
| Related Symbols & Kernel Entries |