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Proof step 51 from proof prepost-update (previous step)

kar[m3 / 2] = key-index(key0, m2), kar[m3 + 1] = key-index(key1, m), ar[m] = elemindex(a, m3 + 1), 2exp-size(# kar), m3 + 1 < # kar, key < key0, key < key1, m3 + 1 < m0, heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar, m0), key-index(key1, m) ∈ keyset(kar, m0), m0 ≤ # kar ⊦ # keyset(kar, m0) = 0, keyset(kar, m0) = ∅, ∀ m. m < m0 ∧ m ≠ 0 → ¬ kar[m3 + 1, key-index(key0, m2)][m].key < kar[m3 + 1, key-index(key0, m2)][(m - 1) / 2].key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
ar[m] = elemindex(a, m3 + 1), kar[m3 + 1] = key-index(key1, m), kar[m3 / 2] = key-index(key0, m2), 2exp-size(# kar), kar[m3 + 1, key-index(key0, m2)][m1].key < kar[m3 + 1, key-index(key0, m2)][(m1 - 1) / 2].key, m1 < m0, m3 + 1 < m0, key < key1, key < key0, m3 + 1 < # kar, m1 < # kar, heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar, m0), key-index(key1, m) ∈ keyset(kar, m0), m0 ≤ # kar ⊦ # keyset(kar, m0) = 0, keyset(kar, m0) = ∅, m1 = 0

Rule argument

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat