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Proof step 2 from proof uint2bits-2potrec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
0 ≤ i, 2 ^ i < j ⊦ uint2bits(j % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j).rest))
Proof step 4:
¬(0 ≤ i ∧ 2 ^ i < j), 0 ≤ i, 2 ^ i ≤ j ⊦ uint2bits(j) = uint2bits(j / 2 ^ i) + fillsgn(i→n(i) + 1, uint2bits(j % 2 ^ i)).rest
Proof step 5:
0 ≤ i ∧ 2 ^ i < j, 0 ≤ i, 2 ^ i ≤ j ⊦ uint2bits(j) = uint2bits(j / 2 ^ i) + fillsgn(i→n(i) + 1, sgn(false ' + lastn(i→n(i), uint2bits(j).rest))).rest

Rule argument

name: uint2bits-mod2pot rotate: F subst: [i, j] → [i, j]

Additional information

Used terms: i, j