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Proof step 8 from proof int2bits-mod2pot (previous step)

0 ≤ j, 0 ≤ i, j0 < 2 ^ i, 0 ≤ j0, 0 < j, 2 ^ i ≤ j * 2 ^ i + j0, 0 < j * 2 ^ i + j0, 0 < 2 ^ i ⊦ uint2bits(j) + fillsgn(i→n(i) + 1, uint2bits((j * 2 ^ i + j0) % 2 ^ i)).rest = int2bits(j) + fillsgn(i→n(i) + 1, int2bits(j0)).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 10:
0 ≤ j, 0 ≤ j, 0 ≤ i, j0 < 2 ^ i, 0 ≤ j0, 0 < j, 2 ^ i ≤ j * 2 ^ i + j0, 0 < j * 2 ^ i + j0, 0 < 2 ^ i ⊦ uint2bits(j) + fillsgn(i→n(i) + 1, uint2bits((j * 2 ^ i + j0) % 2 ^ i)).rest = uint2bits(j) + fillsgn(i→n(i) + 1, int2bits(j0)).rest

Rule argument

name: int2bits-pos rotate: F subst: [i] → [j]

Additional information

Used terms: j