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Circular proofs do not establish a statement

Lax755887.CircularClaims · concepts/Lax755887/CircularClaims.lean · lax-755887

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    Natural Language Statement

    Theorem

    Two false claims admit derivations from each other and from themselves. None has a proof grounded in the background axioms. This additional control tests the least-fixed-point interpretation of the proof network.

    Concept map
    1 concept
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    Open claimThis concept
    Evidence

    This concept declares 2 statements. Each proof establishes one of them relative to its assumptions.

    1 first open

    2 second open

    Lean source view on GitHub

    1
    2
    3/-!
    4---
    5title: Circular proofs do not establish a statement
    6type: theorem
    7---
    8Two false claims admit derivations from each other and from themselves. None has a proof grounded in the background axioms. This additional control tests the least-fixed-point interpretation of the proof network.
    9-/
    10
    11namespace Lax755887.CircularClaims
    12
    13axiom first : False
    14axiom second : False
    15
    16end Lax755887.CircularClaims
    17
    Show Proof Attempt 1Show Proof Attempt 2Show Proof Attempt
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