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Proof step 69 from proof uint2bits-mod2pot (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
j % 2 = 0, uint2bits((j / 2) % 2 ^ i0) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest)), 0 < (j / 2) % 2 ^ i0, 0 ≤ i0, 0 < j, 2 ^ i0 * 2 < j, ∀ 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) + false ' = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest) + false '), ~1 = i0, j = 1

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ 2 * i ≠ 1;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ (i * 2) % 2 = 0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;%j ≠ 0 ⊦ (i * j) / j = i;