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Proof step 83 from proof prepost-bubble-up (previous step)

kar[(n1 - 1) / 2] = key-index(key0, m1), kar[n1] = key-index(key, m0), ar0 = ar1, bh0 = bin-heap(kar, m2), n = n0, bh.ar[n].key < bh.ar[(n - 1) / 2].key, n1 < # kar, n1 < m2, bubble-up-inv(n, bh, ar, bin-heap(kar, m2), ar0), no-dups-idx(kar, m2), valid-idx(kar, ar1, m2), m2 ≤ # kar, n ≠ 0 → n < # bh.ar ∧ (n - 1) / 2 < # bh.ar ∧ 2 ≠ 0 ∧ n ≥ 1, n1 ≠ 0 ∧ key < key0 → heap-order(kar[n1, key-index(key0, m1)], m2), n1 = 0 ∨ ¬ key < key0 → heap-order(kar, m2) ⊦ n = 0, ((n - 1) / 2 < # bh.ar ∧ 2 ≠ 0 ∧ n ≥ 1) ∧ n < # bh.ar

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: bubble-up-inv: ⊦ bubble-up-inv(n, bh, ar, bh0, ar0) ↔ n < bh.size ∧ bh.size ≤ # bh.ar ∧ # bh.ar = # bh0.ar ∧ bh.size = bh0.size ∧ id-idx(ar0, ar) ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar, bh.size) ∧ ( n = 0 ∨ ¬ bh.ar[n].key < bh.ar[(n - 1) / 2].key → heap-order(bh.ar, bh.size)) ∧ ( n ≠ 0 ∧ bh.ar[n].key < bh.ar[(n - 1) / 2].key → heap-order(bh.ar[n, bh.ar[(n - 1) / 2]], bh.size)) ∧ keyset(bh.ar, bh.size) = keyset(bh0.ar, bh0.size);% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ bin-heap(kar, m).size = m; (s)% ⊦ bin-heap(kar, m).ar = kar; (s)