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Proof step 31 from proof cast-help-comm (previous step)

# int2bits(j) < i→n(i), i ≤ i0, 1 < i0, 0 < i0, 0 < i, i < i0 ⊦ i = 0, i0 = 0, bits2int(lastn(i→n(i), fillsgn(i→n(i0), int2bits(j)))) = bits2int(lastn(i→n(i0), fillsgn(i→n(i0), mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j))))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j), i→n(i0)] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;% ⊦ n < m → (m - n) + n = m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ i→n(i) ≤ i→n(j) ↔ abs(i) ≤ abs(j);% ⊦ 0 < j → abs(j) = j;% ⊦ 1 < i → abs(i) = i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ n < m → m - n ≠ 0; Used terms: mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j), i→n(i0)