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Proof step 2 from proof shiftzero-max-neg-01 (previous step)

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

User applied rule induction

And obtained the following new goals

Proof step 3:
0 < j ∧ i < 0 ∧ 2 ^ (n→i(n) - j) ≤ >>>(n, i, j) ∧ j ≤ n→i(n) ∧ # int2bits(i) ≤ n, ∀ n, i, j0. i→n(j0) < i→n(j) → 0 < j0 ∧ i < 0 ∧ 2 ^ (n→i(n) - j0) ≤ >>>(n, i, j0) ∧ j0 ≤ n→i(n) ∧ # int2bits(i) ≤ n → n = 0 ⊦ n = 0

Rule argument

indvar: i→n(j) wfpred: <

Additional information

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