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Proof step 30 from proof intshiftrsign32 (previous step)

32 = (n2 + n1) + i→n(band(j, 31)), 32 = n1 + # int2bits(i), # int2bits(i) = i→n(band(j, 31)) + n2, band(j, 31) ≤ 32, # int2bits(i) ≤ 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, n2, int2bits(i))), n2 = 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, i→n(band(j, 31))), # int2bits(i)] flags: rewrite

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%mk-len: ⊦ # mklist(boolvar, n) = n; from specification list-last[bitlista]%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%abs-zero: ⊦ i→n(i) = 0 ↔ i = 0; from specification intnat%l-02: ⊦ ¬ m + n < m; from specification nat-basic2 Used terms: int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))), # int2bits(i)