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

0 ≤ i ⊦ band(j, i) = bits2uint(fix(# int2bits(i) - 1, int2bits(j))), ∀ i0. i ≠ 2 ^ i0 - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 ≤ i0 ⊦ band(j, 2 ^ i0 - 1) = bits2uint(fix(i→n(i0), int2bits(j)))

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 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;