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Proof step 25 from proof intshiftrsign32 (previous step)

32 = n0 + i→n(band(j, 31)), 32 = n1 + # int2bits(i), n1 < n0, band(j, 31) ≤ 32, # int2bits(i) ≤ 32 ⊦ 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))), band(j, 31) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del inst: bitlista name: sublist-append-02 seq: ⊦ # bits ≤ m → sublist(0, m, bits + bits0) = bits + sublist(0, m - # bits, bits0) subst: [bits0, bits, m] → [int2bits(i), mklist(¬ 0 ≤ i, n1), n0] flags: rewrite

Additional information

Used simplifier rules: mk-len: ⊦ # mklist(boolvar, n) = n; from specification list-last[bitlista]%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1 Used terms: int2bits(i), mklist(¬ 0 ≤ i, n1), n0