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bff4ec7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | import Algorithms.huffman_encoding.lean.spec_lib
namespace Algorithms.huffman_encoding.lean
open AUXLib MaxMinLib
def HuffmanResidualOptimum (input live : List Int) (accumulated : Int) : Prop :=
sum live = sum input ∧ ∃ remaining, HuffmanOptimalCost live remaining ∧ HuffmanOptimalCost input (accumulated + remaining)
def HuffmanProgress (input scratch : List Int) (active accumulated : Int) : Prop :=
HuffmanResidualOptimum input (sublist 0 active scratch) accumulated
def HuffmanMinScan (scratch : List Int) (scanned best : Int) : Prop :=
∀ k, (0 ≤ k ∧ k < scanned) → Znth best scratch 0 ≤ Znth k scratch 0
def HuffmanFirstHeld (input scratch : List Int) (active held accumulated : Int) : Prop :=
∃ prior_live, List.Perm prior_live (held :: sublist 0 active scratch) ∧
(∀ weight, weight ∈ prior_live → held ≤ weight) ∧ HuffmanResidualOptimum input prior_live accumulated
def HuffmanPairReady (input scratch : List Int) (active first second accumulated : Int) : Prop :=
∃ prior_live, List.Perm prior_live (first :: second :: sublist 0 active scratch) ∧
(∀ weight, weight ∈ prior_live → first ≤ weight) ∧
(∀ weight, weight ∈ (second :: sublist 0 active scratch) → second ≤ weight) ∧
HuffmanResidualOptimum input prior_live accumulated
end Algorithms.huffman_encoding.lean
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