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Proof step 6 from proof uint2bits-div2pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ n ≠ 0 → butlastn(n, bits + boolvar ') = butlastn(n -1, bits)
Proof step 8:
¬ i→n(i) ≠ 0, 0 < j, 2 ^ i ≤ j, 0 ≤ i, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i ≤ j0 → uint2bits(j0 / 2 ^ i) = butlastn(i→n(i), uint2bits(j0)) ⊦ j = 1, uint2bits(j / 2 ^ i) = butlastn(i→n(i), uint2bits(j / 2) + (j % 2 = 1)')
Proof step 11:
i→n(i) ≠ 0, 0 < j, 2 ^ i ≤ j, 0 ≤ i, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i ≤ j0 → uint2bits(j0 / 2 ^ i) = butlastn(i→n(i), uint2bits(j0)) ⊦ j = 1, uint2bits(j / 2 ^ i) = butlastn(i→n(i) -1, uint2bits(j / 2))

Rule argument

seq: ⊦ n ≠ 0 → butlastn(n, bits + boolvar ') = butlastn(n -1, bits) subst: [boolvar, bits, n] → [j % 2 = 1, uint2bits(j / 2), i→n(i)] rotate: F spec: list-last inst: bitlista name: blastN-rec

Additional information

Used terms: j % 2 = 1, uint2bits(j / 2), i→n(i)