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Proof step 13 from proof shiftright-rec-pos (previous step)

0 ≤ i, 0 ≤ i0 ⊦ bits2int(firstn(# int2bits(i), (mklist(false, i→n(i0)) + false ') + int2bits(i))) = bits2int(sublist(0, # int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ sublist(m, n, bits) = firstn(n, restn(m, bits))
Proof step 15:
0 ≤ i, 0 ≤ i0 ⊦ bits2int(firstn(# int2bits(i), (mklist(false, i→n(i0)) + false ') + int2bits(i))) = bits2int(firstn(# int2bits(i / 2), restn(0, mklist(false, i→n(i0)) + int2bits(i / 2))))

Rule argument

seq: ⊦ sublist(m, n, bits) = firstn(n, restn(m, bits)) subst: [bits, n, m] → [mklist(false, i→n(i0)) + int2bits(i / 2), # int2bits(i / 2), 0] rotate: F spec: list-del inst: bitlista name: sublist-def

Additional information

Used terms: mklist(false, i→n(i0)) + int2bits(i / 2), # int2bits(i / 2), 0