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Proof step 8 from proof shiftright-rec-neg (previous step)

i < 0 ⊦ j = 0, bits2int(sublist(0, # int2bits(i), mklist(true, i→n(j)) + int2bits(i))) = bits2int(sublist(0, # 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 9:
⊦ j < ~1 → int2bits(j) = int2bits((j - 1) / 2) + int2bits(j % 2)
Proof step 10:
¬ i < ~1, i < 0 ⊦ j = 0, bits2int(sublist(0, # int2bits(i), mklist(true, i→n(j)) + int2bits(i))) = bits2int(sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(abs(j) - 1)) + int2bits((i - 1) / 2)))
Proof step 31:
i < ~1, i < 0 ⊦ j = 0, bits2int(sublist(0, #(int2bits((i - 1) / 2) + int2bits(i % 2)), mklist(true, i→n(j)) + int2bits((i - 1) / 2) + int2bits(i % 2))) = bits2int(sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(abs(j) - 1)) + int2bits((i - 1) / 2)))

Rule argument

seq: ⊦ j < ~1 → int2bits(j) = int2bits((j - 1) / 2) + int2bits(j % 2) subst: [j] → [i] rotate: F spec: int2bits inst: name: int2bits-rec-neg-01

Additional information

Used terms: i