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Proof step 5 from proof cast-mod-neg-high (previous step)

2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), 0 < i, j < 0, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < j % 2 ^ i ⊦ cast(i, j) = j % 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ cast(i, j) = bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j))))
Proof step 7:
2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), 0 < i, j < 0, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < j % 2 ^ i ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))) = j % 2 ^ i

Rule argument

name: cast-def rotate: F subst: [j, i] → [j, i]

Additional information

Used terms: j, i