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Proof step 19 from proof intshiftrsign-rec-pos (previous step)

i0 < 31, 0 ≤ i, 0 ≤ i0, i ≤ 1 ⊦ bits2int(sublist(0, # int2bits(i), (false ' + mklist(false, i→n(i0))) + int2bits(i))) = bits2int(sublist(0, # int2bits(i / 2), mklist(false, i→n(i0 % 32)) + int2bits(i / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ abs(i) < j → i % j = i
Proof step 21:
abs(i0) < 32, i0 < 31, 0 ≤ i, 0 ≤ i0, i ≤ 1 ⊦ bits2int(sublist(0, # int2bits(i), (false ' + mklist(false, i→n(i0))) + int2bits(i))) = bits2int(sublist(0, # int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2)))

Rule argument

seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [32, i0] rotate: F spec: int-div inst: name: mod-zero-05

Additional information

Used simplifier rules: ⊦ 0 ≤ i → abs(i) = i;%j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0); Used terms: 32, i0