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Proof step 38 from proof prepost-resize (previous step)

2exp-size(# kar), 2exp-size(n0), m < n0, m < minsize, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, minsize ≤ n0 ⊦ m ≤ # copy(kar, 0, mkkeyarray(n0), 0, m) ∧ (∀ m0. m0 < m → copy(kar, 0, mkkeyarray(n0), 0, m)[m0].idx < # ar ∧ ar[copy(kar, 0, mkkeyarray(n0), 0, m)[m0].idx].idx = m0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
2exp-size(n0), 2exp-size(# kar), m0 + 1 < n0, m0 + 1 < minsize, m < minsize, m < n0, m0 < m, m0 < minsize, m0 < n0, m0 < # kar, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), minsize ≤ n0, m ≤ # kar ⊦ copy(kar, 0, mkkeyarray(n0), 0, m)[m0].idx < # ar ∧ ar[copy(kar, 0, mkkeyarray(n0), 0, m)[m0].idx].idx = m0

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → m ≤ n; (s)% ⊦ # mkkeyarray(n) = n; (s)% ⊦ # copy(kar, m, kar0, m0, n) = # kar0; (s)