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Proof step 53 from proof prepost-resize (previous step)

m0 = m1 + 1, 2exp-size(# kar), 2exp-size(n0), m0 < # kar, m0 < n0, m0 < minsize, m < n0, m < minsize, m0 < m, copy(kar, 0, mkkeyarray(n0), 0, m)[m0].key < copy(kar, 0, mkkeyarray(n0), 0, m)[m1 / 2].key, m0 + 1 < minsize, m0 + 1 < n0, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, minsize ≤ n0 ⊦ m0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
2exp-size(# kar), 2exp-size(n0), m1 + 1 < # kar, m1 + 1 < minsize, m < n0, m < minsize, m1 + 1 < m, copy(kar, 0, mkkeyarray(n0), 0, m)[m1 + 1].key < copy(kar, 0, mkkeyarray(n0), 0, m)[m1 / 2].key, m1 + 1 < n0, 2 + m1 < n0, 2 + m1 < minsize, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, minsize ≤ n0 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)