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Proof step 9 from proof bin-heap-inv-cleanup-lpt (previous step)

⊦ bin-heap(kar, m).size ≤ # bin-heap(kar, m).ar ∧ no-dups-idx(bin-heap(kar, m).ar, bin-heap(kar, m).size) ∧ valid-idx (bin-heap(kar, m).ar, lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp)), bin-heap(kar, m).size) ∧ 2exp-size(# bin-heap(kar, m).ar) ∧ heap-order(bin-heap(kar, m).ar, bin-heap(kar, m).size) ↔ m ≤ # kar ∧ no-dups-idx(kar, m) ∧ valid-idx(kar, lpt, m) ∧ 2exp-size(# kar) ∧ heap-order(kar, m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
2exp-size(# kar), heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ valid-idx(kar, lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp)), m) ↔ valid-idx(kar, lpt, m)

Rule argument

Additional information

Used simplifier rules: ⊦ bin-heap(kar, m).ar = kar; (s)% ⊦ bin-heap(kar, m).size = m; (s)