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Proof step 33 from proof prepost-update (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 34:
kar[m1] = key-index(key1, m), ar[m] = elemindex(a, m1), kar[m1, key-index(key, m)][(m1 - 1) / 2] = key-index(key0, m2), m3 = m4 + 1, 2exp-size(# kar), m3 < # kar, key < key1, m1 < # kar, m1 < m0, m3 < m0, kar[m1, key-index(key, m)][m3].key < kar[m1, key-index(key, m)][m4 / 2].key, heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar, m0), key-index(key1, m) ∈ keyset(kar, m0), m0 ≤ # kar, m1 = 0 ∨ ¬ key < key0 ⊦ # keyset(kar, m0) = 0, keyset(kar, m0) = ∅, m3 = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m3, m4]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m3, m4