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Proof step 15 from proof shiftzero-max-neg-01 (previous step)

j ≤ n→i(n), 2 ^ (n→i(n) - j) ≤ >>>(n, ~1, j), 0 < j, 1 ≤ 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ j ≠ 0 ∧ n ≠ 0 → >>>(n, ~1, j) = (2 ^ n→i(n) - 1) >> j
Proof step 17:
j ≠ 0 ∧ n ≠ 0, j ≤ n→i(n), 2 ^ (n→i(n) - j) ≤ (2 ^ n→i(n) - 1) >> j, 0 < j, 1 ≤ 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

name: shiftzero-minus-one rotate: F subst: [j, n] → [j, n]

Additional information

Used terms: j, n