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Proof step 7 from proof band-011x-is-unsigned-01 (previous step)

¬(abs(j) ≤ 2 ^ (i - 1) ∧ 0 < i), abs(j) ≤ 2 ^ n→i(1 + i→n(i) - 2), 0 < i ⊦ band(j, 2 ^ i - 1) = bits2uint(fillsgn(i→n(i), int2bits(j)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
i ≤ n→i(1 + i→n(i) - 2), abs(j) ≤ 2 ^ n→i(1 + i→n(i) - 2), 0 < i, 2 ^ (i - 1) < abs(j) ⊦ band(j, 2 ^ i - 1) = bits2uint(fillsgn(i→n(i), int2bits(j))), 1 + i→n(i) - 2 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < n ↔ n ≠ 0;%0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n;% ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i - j < i0 ↔ i < j + i0;%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;