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Sibling proof with the conclusion on the right

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

proven

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    Natural Language Statement

    Theorem

    Three numbered statements, where statement 3 is proved from statements 1 and 2 of the same concept. This is the plain sibling-proof shape: the turnstile sits below the rightmost dock and both of its assumption arrows come from docks to its left.

    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 right
    7type: theorem
    8---
    9Three numbered statements, where statement 3 is proved from statements 1 and 2
    10of the same concept. This is the plain sibling-proof shape: the turnstile sits
    11below the rightmost dock and both of its assumption arrows come from docks to
    12its left.
    13
    14# Formalization notes
    15
    16The three rungs are chosen so that the composite really is the composite:
    1712→1112 \to 11 followed by 11→1011 \to 10 gives 12→1012 \to 10.
    18-/
    19
    20namespace Lax771644.SiblingConclusionRight
    21
    22/-- Descent from stage 12 to stage 11. -/
    23axiom s1 : Foundations.Descent 12 11
    24
    25/-- Descent from stage 11 to stage 10. -/
    26axiom s2 : Foundations.Descent 11 10
    27
    28/-- Descent from stage 12 to stage 10, the composite of the two rungs above. -/
    29axiom s3 : Foundations.Descent 12 10
    30
    31end Lax771644.SiblingConclusionRight
    32
    Show ProofShow ProofShow Proof
    Formalization notes

    The three rungs are chosen so that the composite really is the composite: 12→1112 \to 11 followed by 11→1011 \to 10 gives 12→1012 \to 10.

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    From Mathlib

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