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Proof step 23 from proof always-noincrease-stable (previous step)

□ (A'' ≪ A ∨ A'' = A), ¬ a0 ≪ a ∧ a0 ≠ a ∨ n = N +1 ∧ N = N'' +1 until (¬ A ≪ a ∧ A ≠ a), a = a0, m = n, boolvar → a0 = a1 ∧ n = n0, A ≪ a0 ∨ A = a0, \A ∀ N, A, a. N < m → □ (A'' ≪ A ∨ A'' = A) ∧ a = A → ¬ N = N'' +1 until (¬ A ≪ a ∧ A ≠ a) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
N = N'' + 1 until (¬ A ≪ a0 ∧ A ≠ a0), □ (A'' ≪ A ∨ A'' = A), n = N + 1, boolvar → a0 = a1 ∧ N + 1 = n0, A ≪ a0 ∨ A = a0, \A ∀ N, A, a. N < n → □ (A'' ≪ A ∨ A'' = A) ∧ a = A → ¬ N = N'' +1 until (¬ A ≪ a ∧ A ≠ a) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)% ⊦ ¬ a ≪ a; (s)