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Proof step 4 from proof band-011x-is-unsigned-01 (previous step)

abs(j) ≤ 2 ^ n→i(# int2bits(i0) - 2), 0 < i0 ⊦ band(j, i0) = bits2uint(fillsgn(# int2bits(i0) - 1, int2bits(j))), ∀ i. i0 ≠ 2 ^ i - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
abs(j) ≤ 2 ^ n→i(1 + i→n(i) - 2), 0 < i ⊦ band(j, 2 ^ i - 1) = bits2uint(fillsgn(i→n(i), int2bits(j)))

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ 1 < 2 ^ i ↔ 0 < i;% ⊦ i < j → ¬ j < i;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ 0 + m = m;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;%0 ≤ i ⊦ int2bits(2 ^ i - 1) = false ' + mklist(true, i→n(i));% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < 0 → 2 ^ i = 0;