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Proof step 12 from proof always-noincrease-stable (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 13:
□ A = a, boolvar → a = a1 ∧ n = n0, \A ∀ N, A, a. N < n → □ A = a → ¬ N = N'' +1 until A'' ≠ A ⊦ A = a
Proof step 15:
N = N'' + 1 until A'' ≠ A, □ A = a, n = N + 1, boolvar → a = a1 ∧ n = n0, \A ∀ N, A, a. N < n → □ A = a → ¬ N = N'' +1 until A'' ≠ A ⊦

Rule argument

pos: left 2

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