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Proof step 11 from proof prepost-get-min (previous step)

kar[0] = key-index(key0, m0), 2exp-size(# kar), heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar ⊦ # kar = 0, # keyset(kar, m) = 0, keyset(kar, m) = ∅, ∃ key. key-index(key, m0) ∈ keyset(kar, m) ∧ (∀ ki. ki ∈ keyset(kar, m) → ¬ ki.key < key)

User applied rule exists right

And obtained the following new goals

Proof step 12:
kar[0] = key-index(key0, m0), 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-index(key0, m0) ∈ keyset(kar, m) ∧ (∀ ki. ki ∈ keyset(kar, m) → ¬ ki.key < key0)

Rule argument

pos: right 4 terms: key0 abort: F discard: T computed: T

Additional information

Used terms: key0