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Proof step 22 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 ⊦ ∀ m0, m1. m0 < # copy(kar, 0, mkkeyarray(n0), 0, m) ∧ m0 < m ∧ m1 < # copy(kar, 0, mkkeyarray(n0), 0, m) ∧ m1 < m ∧ m0 ≠ m1 → copy(kar, 0, mkkeyarray(n0), 0, m)[m0].idx ≠ copy(kar, 0, mkkeyarray(n0), 0, m)[m1].idx

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
copy(kar, 0, mkkeyarray(n0), 0, m)[m1].idx = copy(kar, 0, mkkeyarray(n0), 0, m)[m0].idx, 2exp-size(n0), 2exp-size(# kar), m0 + 1 < n0, m1 + 1 < n0, m0 + 1 < minsize, m1 < minsize, m1 < # kar, m1 + 1 < minsize, m0 < m, m < minsize, m < n0, m1 < n0, m1 < 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 ⊦ m1 = 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% ⊦ # mkkeyarray(n) = n; (s)% ⊦ # copy(kar, m, kar0, m0, n) = # kar0; (s)