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Proof step 24 from proof not-always-decrease (previous step)

◇ A ≪ a ⊦ ∃ a1. ◇ (a1 = A ∧ A ≪ a)

User applied rule induction

And obtained the following new goals

Proof step 25:
N = N'' +1 until A ≪ a, m = N, \A ∀ N, A, a. N < m → N = N'' +1 until A ≪ a → (∃ a1. ◇ (a1 = A ∧ A ≪ a)) ⊦ ∃ a1. ◇ (a1 = A ∧ A ≪ a)

Rule argument

indvar: ◇ A ≪ a wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: ◇ A ≪ a