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Proof step 38 from proof intshiftrsign32 (previous step)

32 = n1 + # int2bits(i), 32 = n0 + i→n(band(j, 31)), # int2bits(i) ≤ 32, band(j, 31) ≤ 32, n0 ≤ n1 ⊦ band(j, 31) = 0, bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int((¬ 0 ≤ i)')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ n + m ≤ m0 → sublist(n, m, mklist(boolvar, m0) + bits) = mklist(boolvar, m)
Proof step 40:
¬ 0 + # int2bits(i) ≤ i→n(band(j, 31)), 32 = n1 + # int2bits(i), 32 = n0 + i→n(band(j, 31)), # int2bits(i) ≤ 32, band(j, 31) ≤ 32, n0 ≤ n1 ⊦ band(j, 31) = 0, bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int((¬ 0 ≤ i)')
Proof step 45:
0 + # int2bits(i) ≤ i→n(band(j, 31)), 32 = n1 + # int2bits(i), 32 = n0 + i→n(band(j, 31)), # int2bits(i) ≤ 32, band(j, 31) ≤ 32, n0 ≤ n1 ⊦ band(j, 31) = 0, bits2int(mklist(¬ 0 ≤ i, # int2bits(i))) = bits2int((¬ 0 ≤ i)')

Rule argument

spec: list-del inst: bitlista name: sublist-mklist-01 seq: ⊦ n + m ≤ m0 → sublist(n, m, mklist(boolvar, m0) + bits) = mklist(boolvar, m) subst: [bits, m0, boolvar, m, n] → [int2bits(i), i→n(band(j, 31)), ¬ 0 ≤ i, # int2bits(i), 0] flags: rewrite

Additional information

Used terms: int2bits(i), i→n(band(j, 31)), ¬ 0 ≤ i, # int2bits(i), 0