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Proof step 36 from proof prepost-extract-min (previous step)

kar[m0] = key-index(key0, m), kar[0] = key-index(key1, m1), kar[2] = key-index(key2, m2), kar[1] = key-index(key3, m3), 2exp-size(# kar), m0 < # kar, m < # ar1, heap-order(kar, m0 + 1), no-dups-idx(kar, m0 + 1), valid-idx(kar, ar1, m0 + 1), ∀ ki. ki = key-index(key0, m) ∨ ki ∈ keyset(kar, m0) → ¬ ki.key < key, m0 ≠ 1 ∧ key3 < key0 ∨ 2 < m0 ∧ key2 < key0, key-index(key, m1) = key-index(key0, m) ∨ key-index(key, m1) ∈ keyset(kar, m0) ⊦ #(keyset(kar, m0) ++ key-index(key0, m)) = 0, m0 = 0, heap-order(kar[0, (2 < m0 ∧ key2 < key3 ⊃ key-index(key2, m2);key-index(key3, m3))], m0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
kar[1] = key-index(key3, m3), kar[2] = key-index(key2, m2), kar[0] = key-index(key1, m1), kar[m0] = key-index(key0, m), 2exp-size(# kar), m < # ar1, m0 < # kar, heap-order(kar, m0 + 1), no-dups-idx(kar, m0 + 1), valid-idx(kar, ar1, m0 + 1), ∀ ki. ki = key-index(key0, m) ∨ ki ∈ keyset(kar, m0) → ¬ ki.key < key, key-index(key, m1) = key-index(key0, m) ∨ key-index(key, m1) ∈ keyset(kar, m0), m0 ≠ 1 ∧ key3 < key0 ∨ 2 < m0 ∧ key2 < key0 ⊦ #(keyset(kar, m0) ++ key-index(key0, m)) = 0, m0 = 0, heap-order(kar[0, (2 < m0 ∧ key2 < key3 ⊃ key-index(key2, m2);key-index(key3, m3))], m0)

Proof step 36 from proof prepost-extract-min (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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