Proof term

Mathematical statement

Fix a Lean version, imports, environment E and local context Γ. If core term t has propositional type P and the kernel accepts Γ⊢t:P, then t is a proof term for P. A tactic log is a construction trace, not a saved, replayable proof-term receipt.

Representative formula (exact TeX)

T(t)=P

Assumptions

• P has already been elaborated as a proposition in the same environment; term, context, imports and toolchain are fixed.
• The source pulse did not run Lean builds. Its question bank uses a synthetic small propositional type system and receipt flags, producing no Lean formal Evidence.

Symbol scope

• T — type assignment
• t — candidate proof term
• P — propositional type

Intuition, definition, and misconceptions

Under propositions-as-types, a proof of P is a term of type P. Assumptions, function application, pair construction and projections obey context-dependent type constraints.

A successful tactic with no remaining goals generally produces a candidate proof term. A receipt additionally requires saving that term and checking it with the specified kernel and environment.

Kernel acceptance establishes a formal judgment only. Fidelity to the original Chinese statement and inappropriate axioms in imports are separate semantic and trust obligations.

A tactic transcript, zero goals, successful compilation or model self-report is not the same as a recorded kernel-accepted proof term.

Adopted derivation guide

The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.

Prerequisites

• Formal statements in a proof assistant — First fix P and the identity of its environment.
• Mathematical proof — A proof term is a proof instance in a formal system.

Verification boundary

No Lean execution occurred in the source pulse; synthetic type inference is not a Lean kernel receipt and does not become formal Evidence.

not_formalized

This does not mean the content is false; it means no replayable computational or formal evidence is registered yet.

Next obligation

When Lean work for the specified theorem is resumed, pin term, type, environment, imports, axiom inventory and kernel receipt.

Same-source structured data

This page and the interactive view use the same object and existing language edition; this adds no proof or human review.