Lax Lean Archive

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A statement proved from itself

Lax771644.SelfReferentialProof · concepts/Lax771644/SelfReferentialProof.lean · lax-771644

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    Natural Language Statement

    Theorem

    A one-element cycle: the only proof of this statement assumes the statement itself. It stays unproven, and the drawing has to cope with a turnstile whose assumption and conclusion are the same node.

    Concept map
    2 concepts
    100%
    Open claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    Lean source view on GitHub

    1import Mathlib.Data.Nat.Notation
    2import Lax771644.Foundations
    3
    4/-!
    5---
    6title: A statement proved from itself
    7type: theorem
    8---
    9A one-element cycle: the only proof of this statement assumes the statement
    10itself. It stays unproven, and the drawing has to cope with a turnstile whose
    11assumption and conclusion are the same node.
    12
    13# Formalization notes
    14
    15Nothing subtle happens on the Lean side: an axiom may be used to prove a
    16theorem of its own type, and the archive then records the statement in its own
    17assumption set.
    18-/
    19
    20namespace Lax771644.SelfReferentialProof
    21
    22/-- Descent from stage 310 to stage 300. -/
    23axiom selfRung : Foundations.Descent 310 300
    24
    25end Lax771644.SelfReferentialProof
    26
    Show Proof
    Formalization notes

    Nothing subtle happens on the Lean side: an axiom may be used to prove a theorem of its own type, and the archive then records the statement in its own assumption set.

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