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Proof step 10 from proof uint2bits-add-low-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
0 < j, j0 < 0, 0 < i, 0 ≤ j0 + 2 ^ (i - 1), 2 ^ i + j0 < 0 ⊦ j = 1, uint2bits(2 ^ i * j + j0) = uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))

Rule argument

Additional information

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