Ind \(\mathrm{Ind}\) — Successor-Inductive Class Predicate (Ind, AST Constructor: TpInd)
Unary predicate Ind(X) ⟷ ((∅∈X) ∧ ∀(a:Class)((a∈X)→((a∪{a})∈X))) expressing the narrowest Peano successor-inductive property (Entry DefInductiveClass (3.55)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
Ind
\(\mathrm{Ind}\)
|
| Category | Predicate Symbol (Unary Class Predicate) |
| SML AST Constructor | HP (TpInd of 'Class_EXP) [in datatype Truth_p, typetheory.ML:669] |
| Constructor Arguments | 1. Class X : Class |
| Metatype / Signature | Class → Bool |
| Binder Status | No — Unary Predicate Symbol (Narrowest Peano Successor-Inductive Class) |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathrm{Ind} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | Ind(X) ⟷ ((∅ ∈ X) ∧ ∀(a:Class)((a ∈ X) → ((a ∪ {a}) ∈ X))) |
| Related Symbols & Kernel Entries |