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Proof step 4 from proof shiftzero-pos (previous step)

0 ≤ i ⊦ bits2int(sublist(0, # fillsgn(n, int2bits(i)), mklist(false, i→n(j)) + fillsgn(n, int2bits(i)))) = i >> j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ sublist(m, n, bits) = firstn(n, restn(m, bits))
Proof step 6:
0 ≤ i ⊦ bits2int(firstn(# fillsgn(n, int2bits(i)), restn(0, mklist(false, i→n(j)) + fillsgn(n, int2bits(i))))) = i >> j

Rule argument

seq: ⊦ sublist(m, n, bits) = firstn(n, restn(m, bits)) subst: [bits, n, m] → [mklist(false, i→n(j)) + fillsgn(n, int2bits(i)), # fillsgn(n, int2bits(i)), 0] rotate: F spec: list-del inst: bitlista name: sublist-def

Additional information

Used terms: mklist(false, i→n(j)) + fillsgn(n, int2bits(i)), # fillsgn(n, int2bits(i)), 0