Lax Lean Archive

While this submission is a draft, it cannot be used by other submissions.

Two sibling proofs of the same statement

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

proven

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Natural Language Statement

    Theorem

    Statement 3 carries two independent proofs, one from statement 1 and one from statement 2. Two turnstiles point at the same dock.

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

    This concept declares 3 statements. Each proof establishes one of them relative to its assumptions.

    1 s1 proven

    2 s2 proven

    3 s3 proven

    Lean source view on GitHub

    1import Mathlib.Data.Nat.Notation
    2import Lax771644.Foundations
    3
    4/-!
    5---
    6title: Two sibling proofs of the same statement
    7type: theorem
    8---
    9Statement 3 carries two independent proofs, one from statement 1 and one from
    10statement 2. Two turnstiles point at the same dock.
    11
    12# Formalization notes
    13
    14The two routes descend through different intermediate rungs, so they really
    15are two different proofs and not the same term twice.
    16-/
    17
    18namespace Lax771644.TwoProofsOneStatement
    19
    20/-- Descent from stage 62 to stage 61. -/
    21axiom s1 : Foundations.Descent 62 61
    22
    23/-- Descent from stage 62 to stage 60. -/
    24axiom s2 : Foundations.Descent 62 60
    25
    26/-- Descent from stage 62 to stage 55, reachable through either route. -/
    27axiom s3 : Foundations.Descent 62 55
    28
    29end Lax771644.TwoProofsOneStatement
    30
    Show ProofShow ProofShow Proof 1Show Proof 2
    Formalization notes

    The two routes descend through different intermediate rungs, so they really are two different proofs and not the same term twice.

    Builds on
    Used by

    none

    From Mathlib

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above.

    Loading discussion…