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Proof step 18 from proof prepost-resize (previous step)

2exp-size(n0), 2exp-size(# kar), m < minsize, m < n0, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), minsize ≤ n0, m ≤ # kar ⊦ no-dups-idx(copy(kar, 0, mkkeyarray(n0), 0, m), m) ∧ valid-idx(copy(kar, 0, mkkeyarray(n0), 0, m), ar, m) ∧ heap-order(copy(kar, 0, mkkeyarray(n0), 0, m), m)

User applied rule case distinction

And obtained the following new goals

Proof step 19:
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 ⊦ no-dups-idx(copy(kar, 0, mkkeyarray(n0), 0, m), m)
Proof step 35:
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 ⊦ valid-idx(copy(kar, 0, mkkeyarray(n0), 0, m), ar, m)
Proof step 48:
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 ⊦ heap-order(copy(kar, 0, mkkeyarray(n0), 0, m), m)

Rule argument

pos: right 1

Proof step 18 from proof prepost-resize (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information