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Proof step 4 from proof prepost-get-min (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# keyset(kar, m) ≠ 0, keyset(kar, m) ≠ ∅, 2exp-size(# kar), heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar ⊦ ⟪bin_min_heap_get_min#(bin-heap(kar, m); n)⟫ ∃ key. key-index(key, n) ∈ keyset(kar, m) ∧ (∀ ki. ki ∈ keyset(kar, m) → ¬ ki.key < key)

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ s ≠ ∅ → # s ≠ 0; (forward) from specification set-basic[keyindex-set]%size-zero: ⊦ # s ≠ 0 → s ≠ ∅; (forward) from specification set-basic[keyindex-set]