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Proof step 1 from proof keyset-size-bound (conclusion)

m < # kar ⊦ # keyset(kar, m) ≤ m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
m < # keyset(kar, m), m < # kar ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)