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Proof step 57 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) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest) + false ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
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) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest) + false '), (abs((j / 2) % 2 ^ i0) ≠ 1 ∨ (j / 2) % 2 ^ i0 ≠ 2) ∧ ¬ (j / 2) % 2 ^ i0 ≤ 0

Rule argument

Additional information

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