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Proof step 22 from proof intshiftrsign32 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ n + m ≤ # bits → sublist(n, m, bits + bits0) = sublist(n, m, bits)
Proof step 24:
¬ 0 + n0 ≤ # mklist(¬ 0 ≤ i, n1), 32 = n1 + # int2bits(i), 32 = n0 + i→n(band(j, 31)), # int2bits(i) ≤ 32, band(j, 31) ≤ 32 ⊦ band(j, 31) = 0, bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int((¬ 0 ≤ i)' + sublist(0, n0, mklist(¬ 0 ≤ i, n1) + int2bits(i)))
Proof step 37:
0 + n0 ≤ # mklist(¬ 0 ≤ i, n1), 32 = n1 + # int2bits(i), 32 = n0 + i→n(band(j, 31)), # int2bits(i) ≤ 32, band(j, 31) ≤ 32 ⊦ band(j, 31) = 0, bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int((¬ 0 ≤ i)' + sublist(0, n0, mklist(¬ 0 ≤ i, n1)))

Rule argument

spec: list-del inst: bitlista name: sublist-append seq: ⊦ n + m ≤ # bits → sublist(n, m, bits + bits0) = sublist(n, m, bits) subst: [bits0, bits, m, n] → [int2bits(i), mklist(¬ 0 ≤ i, n1), n0, 0] flags: rewrite

Additional information

Used terms: int2bits(i), mklist(¬ 0 ≤ i, n1), n0, 0