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Proof step 7 from proof uint2bits-mod2pot-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
2 ^ i ≤ j * 2 ^ i + j0, 0 ≤ j0, 0 < j, 0 ≤ i, j0 < 2 ^ i, 0 ≤ j ⊦ fillsgn(i→n(i) + 1, uint2bits((j * 2 ^ i + j0) % 2 ^ i)).rest = fillsgn(i→n(i) + 1, uint2bits(j0)).rest

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ 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);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;