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Proof step 24 from proof intshiftrsign-rec-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n < # bits → sublist(0, n + 1, bits) = sublist(0, n, bits) + bits[n] subst: [bits, n] → [ mklist(false, i→n(band(i0 + 1, 31))) + int2bits(i / 2) + (i % 2 = 1)', # int2bits(i / 2)] rotate: F spec: list-del inst: bitlista name: sublist-lenrec-01

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: mklist(false, i→n(band(i0 + 1, 31))) + int2bits(i / 2) + (i % 2 = 1)', # int2bits(i / 2)