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Proof step 32 from proof shiftright-rec-neg (previous step)

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)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ i ≤ 0 → # int2bits(i % 2) = 1
Proof step 34:
i ≤ 0, i < ~1, i < 0 ⊦ j = 0, bits2int(sublist(0, # int2bits((i - 1) / 2) + 1, 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: ⊦ i ≤ 0 → # int2bits(i % 2) = 1 subst: [i] → [i] rotate: F spec: int2bits inst: name: int2bits-mod2-len

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: i