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Proof step 24 from proof always-noincrease-stable (previous step)

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) ⊦

User applied rule apply induction

And obtained the following new goals

Proof step 25:
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) ⊦ ⟨a := A⟩ (N = N'' +1 until (¬ A ≪ a ∧ A ≠ a))

Rule argument

subst: [N, A, a] → [N, A, A]

Additional information

Used simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ ¬ n < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: N, A, A