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Proof step 41 from proof shiftright-rec-neg (previous step)

i < ~1, i < 0 ⊦ j = 0, bits2int(firstn(# int2bits((i - 1) / 2) + 1, mklist(true, i→n(j)) + int2bits((i - 1) / 2) + int2bits(i % 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 42:
⊦ n < # bits → firstn(n, bits) = firstn(n, bits.butlast)
Proof step 43:
¬ # int2bits((i - 1) / 2) + 1 < #(mklist(true, i→n(j)) + int2bits((i - 1) / 2) + int2bits(i % 2)), i < ~1, i < 0 ⊦ j = 0, bits2int(firstn(# int2bits((i - 1) / 2) + 1, mklist(true, i→n(j)) + int2bits((i - 1) / 2) + int2bits(i % 2))) = bits2int(firstn(# int2bits((i - 1) / 2), mklist(true, i→n(abs(j) - 1)) + int2bits((i - 1) / 2)))
Proof step 46:
# int2bits((i - 1) / 2) + 1 < #(mklist(true, i→n(j)) + int2bits((i - 1) / 2) + int2bits(i % 2)), i < ~1, i < 0 ⊦ j = 0, bits2int(firstn(# int2bits((i - 1) / 2) + 1, (mklist(true, i→n(j)) + int2bits((i - 1) / 2) + int2bits(i % 2)).butlast)) = bits2int(firstn(# int2bits((i - 1) / 2), mklist(true, i→n(abs(j) - 1)) + int2bits((i - 1) / 2)))

Rule argument

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

Additional information

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