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Proof step 8 from proof keyset-size-bound (previous step)

m0 < # kar, m0 + 1 < # kar, m0 + 1 < #(keyset(kar, m0) ++ kar[m0]), ¬ m0 < # keyset(kar, m0) ∨ ¬ m0 < # kar ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
m0 + 1 < #(keyset(kar, m0) ++ kar[m0]), m0 + 1 < # kar, m0 < # kar, # keyset(kar, m0) < # kar, # keyset(kar, m0) ≤ m0 ⊦

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)