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Proof step 31 from proof shiftzero-max-neg (previous step)

n→i(n) = i0 + 1, 1 ≤ n, 0 < j, 2 ^ i0 ≤ (2 ^ i0 - 1) >> (j - 1), 0 ≤ i0, ∀ 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) ⊦ j = 0, n = 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

name: shiftright-not-ls-01 subst: [i, j] → [2 ^ i0 - 1, j - 1]

Additional information

Used simplifier rules: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 2 ^ i0 - 1, j - 1