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Proof step 55 from proof shiftright-rec-neg (previous step)

int2bits(i % 2).butlast = [], i < ~1, i < 0 ⊦ i→n(j) + # int2bits(i % 2) = 0, int2bits((i - 1) / 2) + int2bits(i % 2) = [], j = 0, bits2int(firstn(# int2bits((i - 1) / 2) + 1, mklist(true, i→n(j)) + int2bits((i - 1) / 2))) = bits2int(firstn(# int2bits((i - 1) / 2), mklist(true, i→n(abs(j) - 1)) + int2bits((i - 1) / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
⊦ firstn(n + 1, bits) = bits.first + firstn(n, bits.rest)
Proof step 57:
int2bits(i % 2).butlast = [], i < ~1, i < 0 ⊦ i→n(j) + # int2bits(i % 2) = 0, int2bits((i - 1) / 2) + int2bits(i % 2) = [], j = 0, bits2int ((mklist(true, i→n(j)) + int2bits((i - 1) / 2)).first + firstn(# int2bits((i - 1) / 2), (mklist(true, i→n(j)) + int2bits((i - 1) / 2)).rest)) = bits2int(firstn(# int2bits((i - 1) / 2), mklist(true, i→n(abs(j) - 1)) + int2bits((i - 1) / 2)))

Rule argument

seq: ⊦ firstn(n + 1, bits) = bits.first + firstn(n, bits.rest) subst: [bits, n] → [mklist(true, i→n(j)) + int2bits((i - 1) / 2), # int2bits((i - 1) / 2)] rotate: F spec: list-del inst: bitlista name: firstN-rec

Additional information

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