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Proof step 34 from proof uint2bits-mod2pot (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
j % 2 = 1, uint2bits((j / 2) % 2 ^ i0) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest)), 0 ≤ j, 0 < 2 ^ i0, 0 ≤ i0, 0 < j, 2 ^ i0 * 2 < j, (j / 2) % 2 ^ i0 < 0, (j / 2) % 2 ^ i0 < j, (j / 2) % 2 ^ i0 < i0, (j / 2) % 2 ^ i0 + 1 < 2 ^ i0, (j / 2) % 2 ^ i0 + 1 < 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)) ⊦ ~1 = i0, j = 1, uint2bits((j / 2) % 2 ^ i0 * 2 + 1) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest) + true ')

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < j → i % j < j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i +1 = i + 1;% ⊦ i < j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)