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Exchange

Lax149335.Exchange · concepts/Lax149335/Exchange.lean · lax-149335

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    Natural Language Statement

    Lemma

    Lemma 7.5 (Exchange). Every composition of the form drop-lift is equivalent to a composition of the form lift-drop.

    Concept map
    6 concepts
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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    Lean source view on GitHub

    1import Lax149335.LiftsAndDrops
    2import Lax149335.EquationalTheory
    3
    4/-!
    5---
    6title: Exchange
    7type: lemma
    8---
    9**Lemma 7.5 (Exchange).** Every composition of the form drop-lift is equivalent to a
    10composition of the form lift-drop.
    11-/
    12
    13namespace Lax149335.Exchange
    14
    15open Lax149335.Types Lax149335.Terms Lax149335.EquationalTheory Lax149335.LiftsAndDrops
    16
    17/-- **Lemma 7.5.** A drop followed by a lift is provably equivalent to a lift followed by a
    18drop. -/
    19axiom exchange {A B C : Ty} (d : Term A B) (l : Term B C) (hd : IsDrop d) (hl : IsLift l) :
    20 ∃ (D : Ty) (l' : Term A D) (d' : Term D C), IsLift l' ∧ IsDrop d' ∧ (d ⨟ l) ≡ₜ (l' ⨟ d')
    21
    22end Lax149335.Exchange
    23
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