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Proof step 21 from proof always-noincrease-stable (previous step)

□ (A'' ≪ A ∨ A'' = A), a = A ⊦ □ (A ≪ a ∨ A = a)

User applied rule induction

And obtained the following new goals

Proof step 22:
□ (A'' ≪ A ∨ A'' = A), N = N'' +1 until (¬ A ≪ a ∧ A ≠ a), a = A, m = N, \A ∀ N, A, a. N < m → □ (A'' ≪ A ∨ A'' = A) ∧ a = A → ¬ N = N'' +1 until (¬ A ≪ a ∧ A ≠ a) ⊦

Rule argument

indvar: □ (A ≪ a ∨ A = a) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: □ (A ≪ a ∨ A = a)