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Proof step 2 from proof cast-mod-ls-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ cast(i, j) = bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j))))
Proof step 4:
0 ≤ j, j < 2 ^ (i - 1), 0 < i ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))) = j

Rule argument

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

Additional information

Used terms: j, i