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Proof step 5 from proof bin-heap-inv-cleanup-lpt (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
gch = bin-heap(kar, m) ⊦ bin-heap-inv(gch, lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))) ↔ m ≤ # kar ∧ no-dups-idx(kar, m) ∧ valid-idx(kar, lpt, m) ∧ 2exp-size(# kar) ∧ heap-order(kar, m)

Rule argument

spec: bin-min-heap name: elim seq: ⊦ kar = bh.ar ∧ m = bh.size ↔ bh = bin-heap(kar, m) subst: [bh, kar, n] → [gch, kar, n]

Additional information

Used simplifier rules: ⊦ kar = bh.ar ∧ m = bh.size ↔ bh = bin-heap(kar, m); (elim) Used terms: gch, kar, n