Lax Lean Archive

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

Lift-drop factorisation

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

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

    Lemma

    Lemma 7.4 (Lift-drop factorisation). Every aperiodic rational term is provably equivalent to a composition of a lift followed by a drop.

    Concept map
    6 concepts
    100%
    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: Lift-drop factorisation
    7type: lemma
    8---
    9**Lemma 7.4 (Lift-drop factorisation).** Every aperiodic rational term is provably
    10equivalent to a composition of a lift followed by a drop.
    11-/
    12
    13namespace Lax149335.LiftDropFactorisation
    14
    15open Lax149335.Types Lax149335.Terms Lax149335.EquationalTheory Lax149335.LiftsAndDrops
    16
    17/-- **Lemma 7.4.** Every aperiodic term is provably equivalent to a lift followed by a
    18drop. -/
    19axiom lift_drop_factorisation {A B : Ty} (f : Term A B) (hf : IsAperiodic f) :
    20 ∃ (C : Ty) (l : Term A C) (d : Term C B), IsLift l ∧ IsDrop d ∧ f ≡ₜ (l ⨟ d)
    21
    22end Lax149335.LiftDropFactorisation
    23
    Show Proof
    Builds on
    Used by

    none

    From Mathlib

    none

    Discussion

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

    Loading discussion…