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Proof step 34 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((mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j)).first, 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 35:
⊦ n ≠ 0 → ((mklist(boolvar, n) + bits).first ↔ boolvar)
Proof step 36:
i→n(i) - # int2bits(j) ≠ 0, # 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)))

Rule argument

seq: ⊦ n ≠ 0 → ((mklist(boolvar, n) + bits).first ↔ boolvar) subst: [bits, n, boolvar] → [int2bits(j), i→n(i) - # int2bits(j), ¬ 0 ≤ j] rotate: F spec: list-last inst: bitlista name: mk-first

Additional information

Used simplifier rules: ⊦ n < m → m - n ≠ 0; Used terms: int2bits(j), i→n(i) - # int2bits(j), ¬ 0 ≤ j