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Proof step 93 from proof prepost-extract-min (previous step)

kar[0] = key-index(key1, m), 2exp-size(# kar), no-dups-idx(kar, 1), valid-idx(kar, ar, 1), 1 ≤ # kar ⊦ # kar = 0, ∃ key0. key-index(key0, m) = key-index(key1, m) ∧ ∅ = (∅ ++ key-index(key1, m)) -- key-index(key0, m) ∧ ¬ key1 < key0

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: key1

Additional information

Used simplifier rules: ⊦ (s ++ ki) -- ki = s -- ki; (s)% ⊦ ∅ -- ki = ∅; (s)% ⊦ ¬ key < key; (s) Used terms: key1