injective \(\mathrm{injective}\) — Injective Class-Function Predicate (injective, AST Constructor: TpInjective)
Unary predicate asserting that f is a class-function that is one-to-one on Dom(f) (Entry DefInjectiveFunction (3.33)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
injective
\(\mathrm{injective}\)
|
| Category | Predicate Symbol (Unary Class Predicate) |
| SML AST Constructor | HP (TpInjective of 'Class_EXP) [in datatype Truth_p, typetheory.ML:677] |
| Constructor Arguments | 1. Class-function f : Class |
| Metatype / Signature | Class → Bool |
| Binder Status | No — Unary Predicate Symbol (Injectivity) |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathrm{injective} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | (f is injective) ⟷ ((f is a class-function) ∧ ∀(x∈Dom(f))∀(y∈Dom(f))((f(x)=f(y))→(x=y))) |
| Related Symbols & Kernel Entries |