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Proof step 2 from proof keyset-eq-empty (previous step)

bin-heap-inv(bh, ar) ⊦ keyset(bh) = ∅ ↔ bh.size = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
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 ⊦ keyset(bh.ar, bh.size) = ∅ ↔ bh.size = 0

Rule argument

Additional information

Used simplifier rules: keyset: ⊦ keyset(bh) = keyset(bh.ar, bh.size);%bin-heap-inv-def: ⊦ bin-heap-inv(bh, ar) ↔ bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size);