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Proof step 2 from proof uint2bits-add-high-01 (previous step)

1 < j, 0 < j, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 ≤ j0 + 2 ^ i ⊦ uint2bits(j * 2 ^ i + j0) = uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0).rest)

User applied rule cut formula

And obtained the following new goals

Proof step 3:
j * 2 ^ i + j0 = (j - 1) * 2 ^ i + 2 ^ i + j0, 1 < j, 0 < j, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 ≤ j0 + 2 ^ i ⊦ uint2bits(j * 2 ^ i + j0) = uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0).rest)

Rule argument

fma: j * 2 ^ i + j0 = (j - 1) * 2 ^ i + 2 ^ i + j0

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i * j + i = i * (j + 1);% ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j = i + i0 ↔ j = i0; Used formulas: j * 2 ^ i + j0 = (j - 1) * 2 ^ i + 2 ^ i + j0