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Proof step 10 from proof prepost-update (previous step)

kar[m1] = key-index(key0, m), ar[m] = elemindex(a, m1), ar0 = ar, bh = bin-heap(kar, m0), n = m1, 2exp-size(# kar), heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar, m0), key-index(key0, m) ∈ keyset(kar, m0), m0 ≤ # kar ⊦ # keyset(kar, m0) = 0, keyset(kar, m0) = ∅, n < bh.size

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
ar[m] = elemindex(a, m1), kar[m1] = key-index(key0, m), 2exp-size(# kar), heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar, m0), key-index(key0, m) ∈ keyset(kar, m0), m0 ≤ # kar, m0 ≤ m1 ⊦ # keyset(kar, m0) = 0, keyset(kar, m0) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ bin-heap(kar, m).size = m; (s)