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Proof step 11 from proof intshiftrsign-rec-neg (previous step)

0 ≤ j, 0 < j, i < 0, j < 32 ⊦ bits2int(sublist(0, # int2bits(i), mklist(true, i→n(j % 32)) + int2bits(i))) = bits2int(sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(band(j - 1, 31))) + int2bits((i - 1) / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ abs(i) < j → i % j = i
Proof step 13:
abs(j) < 32, 0 ≤ j, 0 < j, i < 0, j < 32 ⊦ bits2int(sublist(0, # int2bits(i), mklist(true, i→n(j)) + int2bits(i))) = bits2int(sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(band(j - 1, 31))) + int2bits((i - 1) / 2)))

Rule argument

seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [32, j] rotate: F spec: int-div inst: name: mod-zero-05

Additional information

Used simplifier rules: ⊦ 0 < j → abs(j) = j;%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); Used terms: 32, j