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Proof step 1 from proof shiftzero-max-neg (conclusion)

⊦ i < 0 ∧ # int2bits(i) ≤ n ∧ 0 < j ∧ n ≠ 0 → >>>(n, i, j) < 2 ^ (n→i(n) - 1)

User applied rule induction

And obtained the following new goals

Proof step 2:
true, ∀ n, i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ # int2bits(i) ≤ n ∧ 0 < j0 ∧ n ≠ 0 → >>>(n, i, j0) < 2 ^ (n→i(n) - 1) ⊦ i < 0 ∧ # int2bits(i) ≤ n ∧ 0 < j ∧ n ≠ 0 → >>>(n, i, j) < 2 ^ (n→i(n) - 1)

Rule argument

indvar: i→n(j) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(j)