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Proof step 20 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ no-dups-idx(kar, n) ↔ (∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx)
Proof step 22:
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

Rule argument

spec: bin-min-heap-inv name: no-dups-idx seq: ⊦ no-dups-idx(kar, n) ↔ (∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx) subst: [n, kar] → [m, copy(kar, 0, mkkeyarray(n0), 0, m)] flags: <all paths>

Additional information

Used terms: m, copy(kar, 0, mkkeyarray(n0), 0, m)