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Proof step 9 from proof prepost-get-min (previous step)

bh = bin-heap(kar, m), 2exp-size(# kar), 0 < # bh.ar, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar ⊦ # keyset(kar, m) = 0, keyset(kar, m) = ∅, ∃ key. key-index(key, bh.ar[0].idx) ∈ keyset(kar, m) ∧ (∀ ki. ki ∈ keyset(kar, m) → ¬ ki.key < key)

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), valid-idx(kar, ar, m), m ≤ # kar ⊦ # keyset(kar, m) = 0, # kar = 0, keyset(kar, m) = ∅, ∃ key. key-index(key, kar[0].idx) ∈ keyset(kar, m) ∧ (∀ ki. ki ∈ keyset(kar, m) → ¬ ki.key < key)

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ bin-heap(kar, m).ar = kar; (s)