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Proof step 3 from proof key-set-in (previous step)

2exp-size(# bh.ar), heap-order(bh.ar, bh.size), no-dups-idx(bh.ar, bh.size), valid-idx(bh.ar, ar, bh.size), bh.size ≤ # bh.ar ⊦ ki ∈ keyset(bh.ar, bh.size) ↔ (∃ m. m < bh.size ∧ ki = bh.ar[m])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
bh = bin-heap(kar, m0), 2exp-size(# kar), heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar, m0), m0 ≤ # kar ⊦ ki ∈ keyset(kar, m0) ↔ (∃ m. m < m0 ∧ ki = 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, m] → [bh, kar, m0]

Additional information

Used simplifier rules: ⊦ kar = bh.ar ∧ m = bh.size ↔ bh = bin-heap(kar, m); (elim) Used terms: bh, kar, m0