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Proof step 13 from proof int2bits-mod2pot (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
0 ≤ i, j0 < 2 ^ i, 0 ≤ j0, 0 < j, 2 ^ i ≤ j * 2 ^ i + j0, 0 < j * 2 ^ i + j0, 0 < 2 ^ i, 0 ≤ j ⊦ fillsgn(i→n(i) + 1, uint2bits(j0)).rest = fillsgn(i→n(i) + 1, int2bits(j0)).rest

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0);