⊢ \(\vdash\) — Formal Derivability Turnstile Predicate Symbol (⊢, AST Constructor: TpHolds)
Ternary metatheoretic derivability predicate (𝘞, Γ ⊢ 𝛗) asserting that syntactic formula 𝛗 : Fm is formally derivable in object theory 𝘞 : Theory from hypothesis context Γ : Ctx.
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
⊢
\(\vdash\)
|
| Category | Predicate Symbol (Ternary Metatheoretic Derivability Judgment) |
| SML AST Constructor | HP (TpHolds of ('Theory_EXP * 'Ctx_EXP * 'Truth_Expression_EXP)) [in datatype Truth_p, typetheory.ML:682] |
| Constructor Arguments | 1. Formal theory 𝘞 : Theory; 2. Hypothesis context Γ : Ctx; 3. Formula 𝛗 : Fm |
| Metatype / Signature | Theory × Ctx × Fm → Bool |
| Binder Status | No — Ternary Metatheoretic Derivability Predicate Symbol (𝘞, Γ ⊢ 𝛗) |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \vdash |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | (𝘍, [] ⊢ 𝛙) → ⟦𝛙⟧ |
| Related Symbols & Kernel Entries |