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Finite exposure partitions

Lax342547.PartitionLists · concepts/Lax342547/PartitionLists.lean · lax-342547

proven

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    Natural Language Statement

    Lemma

    A distinct ordering splits into disjoint exposed and remaining index sets, with their exact union and tail cardinality.

    Concept map
    13 concepts
    100%
    Proven claimThis conceptRelated conceptA → B: B builds on ADescendants are omitted for concepts with more than 10 descendants.
    Evidence

    This concept declares 3 statements. Each proof establishes one of them relative to its assumptions.

    1 take_drop_card proven

    2 take_drop_disjoint proven

    3 take_drop_union proven

    Lean source view on GitHub

    1import Lax342547.SmallExposure
    2
    3/-!
    4---
    5title: Finite exposure partitions
    6type: lemma
    7---
    8A distinct ordering splits into disjoint exposed and remaining index sets, with their exact union and tail cardinality.
    9-/
    10
    11namespace Lax342547.PartitionLists
    12
    13
    14
    15axiom take_drop_disjoint {ι : Type} [DecidableEq ι] (l : List ι) (hl : l.Nodup) (t : ℕ) :
    16 Disjoint (l.take t).toFinset (l.drop t).toFinset
    17
    18axiom take_drop_union {ι : Type} [DecidableEq ι] (l : List ι) (t : ℕ) :
    19 (l.take t).toFinset ∪ (l.drop t).toFinset = l.toFinset
    20
    21axiom take_drop_card {ι : Type} [DecidableEq ι] (l : List ι) (hl : l.Nodup)
    22 (b : ℕ) (hb : b ≤ l.length) : (l.drop (l.length-b)).toFinset.card = b
    23
    24end Lax342547.PartitionLists
    25
    Show ProofShow ProofShow Proof
    Builds on
    Used by
    From Mathlib

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