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Proof step 1 from proof uint2bits-div2pot-01 (conclusion)

0 ≤ i, 0 < j, j % 2 ^ i = 0 ⊦ uint2bits(j) = uint2bits(j / 2 ^ i) + mklist(false, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
0 ≤ i, 2 ^ i ≤ j ⊦ uint2bits(j / 2 ^ i) = butlastn(i→n(i), uint2bits(j))
Proof step 3:
¬(0 ≤ i ∧ 2 ^ i ≤ j), 0 ≤ i, 0 < j, j % 2 ^ i = 0 ⊦ uint2bits(j) = uint2bits(j / 2 ^ i) + mklist(false, i→n(i))
Proof step 5:
0 ≤ i ∧ 2 ^ i ≤ j, 0 ≤ i, 0 < j, j % 2 ^ i = 0 ⊦ uint2bits(j) = butlastn(i→n(i), uint2bits(j)) + mklist(false, i→n(i))

Rule argument

name: uint2bits-div2pot rotate: F subst: [i, j] → [i, j]

Additional information

Used terms: i, j