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

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

Rule argument

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

Additional information

Used terms: j, i