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Proof step 1 from proof keyset-size-bound0 (conclusion)

m < # kar ⊦ # keyset(kar, m) = m + 1 ↔ false

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# keyset(kar, m) = m + 1, m < # kar ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%eqle-one: ⊦ m = n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat