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Proof step 9 from proof uint2bits-succ (previous step)

0 ≤ j, 0 < j, ∀ j0. i→n(j0) < i→n(j) → 0 ≤ j0 → uint2bits(j0 + 1) = sgn(false ' + uint2bits(j0) +1) ⊦ j = 1, uint2bits((j + 1) / 2) + ((j + 1) % 2 = 1)' = sgn(false ' + (uint2bits(j / 2) + (j % 2 = 1)')+1)

User applied rule cut formula

And obtained the following new goals

Proof step 10:
j % 2 = 1, 0 ≤ j, 0 < j, ∀ j0. i→n(j0) < i→n(j) → 0 ≤ j0 → uint2bits(j0 + 1) = sgn(false ' + uint2bits(j0) +1) ⊦ j = 1, uint2bits((j + 1) / 2) + ((j + 1) % 2 = 1)' = sgn(false ' + (uint2bits(j / 2) + (j % 2 = 1)')+1)
Proof step 18:
0 ≤ j, 0 < j, ∀ j0. i→n(j0) < i→n(j) → 0 ≤ j0 → uint2bits(j0 + 1) = sgn(false ' + uint2bits(j0) +1) ⊦ j % 2 = 1, j = 1, uint2bits((j + 1) / 2) + ((j + 1) % 2 = 1)' = sgn(false ' + (uint2bits(j / 2) + (j % 2 = 1)')+1)

Rule argument

fma: j % 2 = 1

Additional information

Used formulas: j % 2 = 1