Lax Lean Archive

Restriction of scatter types

Lax185574.ScatterTypeRestriction · concepts/Lax185574/ScatterTypeRestriction.lean · lax-185574

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    Natural Language Statement

    Lemma

    For every partial graph G and q ≥ 1, the function stp_{k+1,q−1} is the restriction of stp_{k,q} to domain(stp_{k+1,q−1}).

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    In the paper

    • page 45 of this submission's paper

    Lean source view on GitHub

    1import Lax185574.ScatterTypes
    2
    3/-!
    4---
    5title: Restriction of scatter types
    6type: lemma
    7---
    8For every partial graph G and q ≥ 1, the function stp_{k+1,q−1} is the
    9restriction of stp_{k,q} to domain(stp_{k+1,q−1}).
    10
    11# Formalization notes
    12
    13q ≥ 1 is written as q + 1. The statement says that domain(stp_{k+1,q})
    14is contained in domain(stp_{k,q+1}) and that the two functions agree on
    15it.
    16-/
    17
    18namespace Lax185574.ScatterTypeRestriction
    19
    20open Lax185574.PartialGraphs Lax185574.ScatterTypes
    21
    22/-- **Restriction of scatter types.** -/
    23axiom stp_restrict {n : ℕ} (G : PartialGraph (Fin n)) (k q : ℕ) :
    24 domain G (k + 1) q ⊆ domain G k (q + 1) ∧
    25 ∀ p ∈ domain G (k + 1) q, value G (k + 1) q p = value G k (q + 1) p
    26
    27end Lax185574.ScatterTypeRestriction
    28
    Show Proof
    Formalization notes

    q ≥ 1 is written as q + 1. The statement says that domain(stp_{k+1,q}) is contained in domain(stp_{k,q+1}) and that the two functions agree on it.

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