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Proof step 50 from proof uint2bits-mod2pot (previous step)

0 ≤ (j / 2) % 2 ^ i0, uint2bits((j / 2) % 2 ^ i0) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest)), j % 2 = 1, 2 ^ i0 * 2 < j, 0 < j, 0 ≤ i0, 0 < 2 ^ i0, 0 ≤ j, 0 < (j / 2) % 2 ^ i0, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ uint2bits((j / 2) % 2 ^ i0) + (((j / 2) % 2 ^ i0 * 2 + 1) % 2 = 1)' = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest) + true '), j = 1, ~1 = i0, (j / 2) % 2 ^ i0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
uint2bits((j / 2) % 2 ^ i0) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest)), j % 2 = 1, 2 ^ i0 * 2 < j, 0 < j, 0 ≤ i0, 0 < 2 ^ i0, 0 ≤ j, 0 < (j / 2) % 2 ^ i0, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ j = 1, ~1 = i0, (j / 2) % 2 ^ i0 = 0, uint2bits((j / 2) % 2 ^ i0) + true ' = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest) + true ')

Rule argument

Additional information

Used simplifier rules: ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 ≤ i → (i * 2 + 1) % 2 = 1;