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Proof step 5 from proof keyset-eq-empty (previous step)

keyset(kar, m) = ∅, 2exp-size(# kar), heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar ⊦ m = 0

User applied rule constructor cut

And closed the goal!

Rule argument

var: m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;% ⊦ m +1 = m + 1; (s)% ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ n < # kar → keyset(kar, n + 1) = keyset(kar, n) ++ kar[n]; (s)% ⊦ ∅ ≠ s ++ ki; (s)