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Proof step 6 from proof uint2bits-pred (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 1 < i → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1)
Proof step 8:
1 < j, 1 < j, 0 < j, 0 ≤ j, ∀ j0. i→n(j0) < i→n(j) → 0 < j0 → uint2bits(j0 - 1) = sgn(bitsinvert(bitsinvert(uint2bits(j0)) +1)) ⊦ uint2bits((j - 1) / 2) + ((j - 1) % 2 = 1)' = sgn(bitsinvert(bitsinvert(uint2bits(j / 2) + (j % 2 = 1)) +1)), j = 2

Rule argument

name: uint2bits-rec rotate: F subst: [i] → [j]

Additional information

Used terms: j