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Proof step 35 from proof intshiftrsign32 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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, int2bits(i)), i→n(band(j, 31)), ¬ 0 ≤ i] flags: rewrite

Additional information

Used simplifier rules: abs-zero: ⊦ i→n(i) = 0 ↔ i = 0; from specification intnat Used terms: sublist(0, n0, int2bits(i)), i→n(band(j, 31)), ¬ 0 ≤ i