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Proof step 39 from proof cast-help-comm (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n)
Proof step 41:
# int2bits(j) < i→n(i), 1 < i0, 0 < i0, 0 < i, i < i0, i ≤ i0 ⊦ mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j) = [], i = 0, i0 = 0, bits2int(lastn(i→n(i), fillsgn(i→n(i0), int2bits(j)))) = bits2int(lastn(i→n(i0), mklist(¬ 0 ≤ j, (i→n(i0) - i→n(i)) + (i→n(i) - # int2bits(j))) + int2bits(j)))

Rule argument

seq: ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n) subst: [n, m, boolvar] → [i→n(i) - # int2bits(j), i→n(i0) - i→n(i), ¬ 0 ≤ j] rotate: T spec: list-last inst: bitlista name: mk-plus

Additional information

Used terms: i→n(i) - # int2bits(j), i→n(i0) - i→n(i), ¬ 0 ≤ j