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Proof step 4 from proof cast-law-shift-snd-zr (previous step)

5 ≤ i, 0 < i, 0 ≤ i ⊦ j0 i>>> j = bits2int(sublist(0, # fillsgn(32, int2bits(j0)), mklist(false, i→n(band(cast(i, j), 31))) + fillsgn(32, int2bits(j0))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
n→i((# int2bits(j0))-1) ≤ i, 0 ≤ j0 ⊦ band(cast(i, j), j0) = band(j, j0)
Proof step 6:
¬(n→i((# int2bits(31))-1) ≤ i ∧ 0 ≤ 31), 5 ≤ i, 0 < i, 0 ≤ i ⊦ j0 i>>> j = bits2int(sublist(0, # fillsgn(32, int2bits(j0)), mklist(false, i→n(band(cast(i, j), 31))) + fillsgn(32, int2bits(j0))))
Proof step 8:
n→i((# int2bits(31))-1) ≤ i ∧ 0 ≤ 31, 5 ≤ i, 0 < i, 0 ≤ i ⊦ j0 i>>> j = bits2int(sublist(0, # fillsgn(32, int2bits(j0)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(j0))))

Rule argument

name: cast-band rotate: F subst: [j0, j, i] → [31, j, i]

Additional information

Used terms: 31, j, i