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Proof step 12 from proof shiftzero-rec-neg-longer (previous step)

i < ~1, 0 < j, 1 < j, i < 0, n ≤ # int2bits((i - 1) / 2) ⊦ i = ~1, bits2int(firstn(# fillsgn(n, int2bits((i - 1) / 2) + (i % 2 ≠ 0)'), mklist(false, i→n(j)) + fillsgn(n, int2bits((i - 1) / 2) + (i % 2 ≠ 0)'))) = bits2int(sublist(0, # int2bits((i - 1) / 2), mklist(false, i→n(j) - 1) + int2bits((i - 1) / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ sublist(m, n, bits) = firstn(n, restn(m, bits))
Proof step 14:
i < ~1, 0 < j, 1 < j, i < 0, n ≤ # int2bits((i - 1) / 2) ⊦ i = ~1, bits2int(firstn(# fillsgn(n, int2bits((i - 1) / 2) + (i % 2 ≠ 0)'), mklist(false, i→n(j)) + fillsgn(n, int2bits((i - 1) / 2) + (i % 2 ≠ 0)'))) = bits2int(firstn(# int2bits((i - 1) / 2), restn(0, mklist(false, i→n(j) - 1) + int2bits((i - 1) / 2))))

Rule argument

seq: ⊦ sublist(m, n, bits) = firstn(n, restn(m, bits)) subst: [bits, n, m] → [mklist(false, i→n(j) - 1) + int2bits((i - 1) / 2), # int2bits((i - 1) / 2), 0] rotate: F spec: list-del inst: bitlista name: sublist-def

Additional information

Used terms: mklist(false, i→n(j) - 1) + int2bits((i - 1) / 2), # int2bits((i - 1) / 2), 0