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Sibling proof with the conclusion on the left

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

proven

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    Natural Language Statement

    Theorem

    The mirror image of the previous concept: statement 1 is proved from statements 2 and 3. The turnstile therefore sits below the leftmost dock while both of its assumption arrows arrive from docks to its right.

    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: Sibling proof with the conclusion on the left
    7type: theorem
    8---
    9The mirror image of the previous concept: statement 1 is proved from statements
    102 and 3. The turnstile therefore sits below the *leftmost* dock while both of
    11its assumption arrows arrive from docks to its right.
    12
    13# Formalization notes
    14
    15Same ladder, different band of rungs, so that the two concepts cannot be
    16confused when both are on screen.
    17-/
    18
    19namespace Lax771644.SiblingConclusionLeft
    20
    21/-- Descent from stage 22 to stage 20, the composite of the two rungs below. -/
    22axiom s1 : Foundations.Descent 22 20
    23
    24/-- Descent from stage 22 to stage 21. -/
    25axiom s2 : Foundations.Descent 22 21
    26
    27/-- Descent from stage 21 to stage 20. -/
    28axiom s3 : Foundations.Descent 21 20
    29
    30end Lax771644.SiblingConclusionLeft
    31
    Show ProofShow ProofShow Proof
    Formalization notes

    Same ladder, different band of rungs, so that the two concepts cannot be confused when both are on screen.

    Builds on
    Used by

    none

    From Mathlib

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