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Cycle, first half

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

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    Natural Language Statement

    Theorem

    Half of a genuine cross-concept cycle: this statement is proved from the statement of CycleBetaCycleBeta, which is in turn proved from this one. Neither becomes proven — the archive's notion of provenness is a least fixed point — so both should be drawn open and inside the grey display-cycle envelope.

    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: Cycle, first half
    7type: theorem
    8---
    9Half of a genuine cross-concept cycle: this statement is proved from the
    10statement of `CycleBeta`, which is in turn proved from this one. Neither becomes
    11proven — the archive's notion of provenness is a least fixed point — so both
    12should be drawn open and inside the grey display-cycle envelope.
    13
    14# Formalization notes
    15
    16The two statements are given the same type, which is the only way two proofs
    17can genuinely stand in for one another; each proof really is the other statement
    18and nothing else.
    19-/
    20
    21namespace Lax771644.CycleAlpha
    22
    23/-- Descent from stage 300 to stage 290. -/
    24axiom alpha : Foundations.Descent 300 290
    25
    26end Lax771644.CycleAlpha
    27
    Show Proof
    Formalization notes

    The two statements are given the same type, which is the only way two proofs can genuinely stand in for one another; each proof really is the other statement and nothing else.

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