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Proof step 6 from proof int2bytes-rec-neg-01 (previous step)

j ≤ ~(2 ^ (i * 8)) ∧ 0 < i * 8 ∧ j % 2 ^ (i * 8) = 0, j % 2 ^ (i * 8) = 0, j + 2 ^ (i * 8) < 0, 0 < i ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + fillsgn(i→n(i * 8 + 1), int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, i2b(0) ').rest

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
j % 2 ^ (i * 8) = 0, 0 < i, j + 2 ^ (i * 8) < 0 ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + mklist(false, i→n(i * 8))) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, i2b(0) ').rest

Rule argument

Additional information

Used simplifier rules: ⊦ (boolvar ' + bits).rest = bits;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + [] = bits;% ⊦ mklist(boolvar, 0) = [];%n ≠ 0 ⊦ mklist(false, (* n)) = false ' + mklist(false, n -1);% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ fillsgn(n + 1, boolvar ') = mklist(boolvar, n + 1);% ⊦ int2bits(0) = false ';% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i * j = j * i;% ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 < i → i→n(i + 1) = i→n(i) + 1;