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Persistent queues — independent controls

Lax755887.PersistentQueueControls · concepts/Lax755887/PersistentQueueControls.lean · lax-755887

proven

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    Natural Language Statement

    Theorem

    These statements use only the background axioms. They record the actual behavior or the valid local calculation, independently of the unchecked contract.

    Concept map
    2 concepts
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    This concept declares 2 statements. Each proof establishes one of them relative to its assumptions.

    1 actual_work proven

    2 dequeue_charge proven

    Lean source view on GitHub

    1import Lax755887.PersistentQueue
    2
    3/-!
    4---
    5title: Persistent queues — independent controls
    6type: theorem
    7---
    8These statements use only the background axioms. They record the actual behavior or the valid local calculation, independently of the unchecked contract.
    9-/
    10
    11namespace Lax755887.PersistentQueueControls
    12
    13open Lax755887.PersistentQueue
    14
    15axiom dequeue_charge (n : ℕ) : amortized (dequeue n) = 1
    16
    17axiom actual_work (n : ℕ) :
    18 totalWork (List.replicate (n + 1) (dequeue n)) = (n + 1) ^ 2
    19
    20end Lax755887.PersistentQueueControls
    21
    Show ProofShow Proof
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