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Proof step 94 from proof prepost-update (previous step)

ar[m] = elemindex(a, m1), kar[m1] = key-index(key0, m), ar0 = ar, bh = bin-heap(kar, m0), n = m1, 2exp-size(# kar), n < bh.size, 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.ar

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < n → n ≠ 0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ bin-heap(kar, m).ar = kar; (s)% ⊦ bin-heap(kar, m).size = m; (s)