Theorem Proving in Lean 4 says that in interactive proving, every step of a calculation has to be justified by appealing to prior definitions and theorems, all the way down to basic axioms and rules.

The exact words it rests on

interactive theorem proving focuses on the verification aspect of theorem proving, requiring that every claim is supported by a proof in a suitable axiomatic foundation. This sets a very high standard: every rule of inference and every step of a calculation has to be justified by appealing to prior definitions and theorems, all the way down to basic axioms and rules.

What the source said when we opened it, on 18 Oct 2026.

The source

Theorem Proving in Lean 4: Introduction
Lean FRO / Lean project

Open the sourcearchived copy

Checked

Checked by the notis newsroom on 18 Oct 2026, against the source above.

In the story

How Lean checks an AI-written proof, and where that stops 18 Oct 2026