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Proof step 9 from proof intshiftrsign32 (previous step)

32 = n0 + i→n(band(j, 31)), # int2bits(i) ≤ 32, band(j, 31) ≤ 32 ⊦ bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int(mklist(¬ 0 ≤ i, i→n(band(j, 31))) + sublist(0, n0, fillsgn(32, int2bits(i))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ n ≠ 0 → bits2int(mklist(boolvar, n) + bits) = bits2int(boolvar ' + bits)
Proof step 11:
¬ i→n(band(j, 31)) ≠ 0, 32 = n0 + i→n(band(j, 31)), # int2bits(i) ≤ 32, band(j, 31) ≤ 32 ⊦ bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int(mklist(¬ 0 ≤ i, i→n(band(j, 31))) + sublist(0, n0, fillsgn(32, int2bits(i))))
Proof step 17:
i→n(band(j, 31)) ≠ 0, 32 = n0 + i→n(band(j, 31)), # int2bits(i) ≤ 32, band(j, 31) ≤ 32 ⊦ bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int((¬ 0 ≤ i)' + sublist(0, n0, fillsgn(32, int2bits(i))))

Rule argument

spec: int2bits inst: name: bits2int-mklist-05 seq: ⊦ n ≠ 0 → bits2int(mklist(boolvar, n) + bits) = bits2int(boolvar ' + bits) subst: [bits, n, boolvar] → [sublist(0, n0, fillsgn(32, int2bits(i))), i→n(band(j, 31)), ¬ 0 ≤ i] flags: rewrite

Additional information

Used terms: sublist(0, n0, fillsgn(32, int2bits(i))), i→n(band(j, 31)), ¬ 0 ≤ i