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Proof step 2 from proof shiftzero-by-one-01 (previous step)

i < ~1, i < 0 ⊦ n = 0, >>>(n, i, 1) = (i - 1) / 2 + 2 ^ n→i(# fillsgn(n, int2bits(i)) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i < ~1 ∧ n ≠ 0 → >>>(n, i, 1) = bits2uint(fillsgn(n -1, int2bits((i - 1) / 2)))
Proof step 4:
i < ~1 ∧ n ≠ 0, i < ~1, i < 0 ⊦ n = 0, bits2uint(fillsgn(n -1, int2bits((i - 1) / 2))) = (i - 1) / 2 + 2 ^ n→i(# fillsgn(n, int2bits(i)) - 1)

Rule argument

name: shiftzero-by-one rotate: F subst: [i, n] → [i, n]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j = i0 ↔ i = i0 + j; Used terms: i, n