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Proof step 86 from proof shiftzero-pos (previous step)

i→n(j) < # int2bits(i), 0 ≤ i, # int2bits(i) < n, i→n(j) < n, i→n(j) + 1 < n, n ≤ (n - i→n(j)) + # int2bits(i), i→n(j) < (n - i→n(j)) + # int2bits(i), i→n(j) + 1 < (n - i→n(j)) + # int2bits(i), (mklist(false, n - # int2bits(i)) + firstn(# int2bits(i) - i→n(j), int2bits(i))).first ⊦ # int2bits(i) = i→n(j), bits2int(mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + firstn(# int2bits(i) - i→n(j), int2bits(i))) = bits2int(firstn(# int2bits(i) - i→n(j), int2bits(i))), n + # int2bits(i) = i→n(j), firstn(# int2bits(i) - i→n(j), int2bits(i)).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 87:
⊦ n ≠ 0 → ((mklist(boolvar, n) + bits).first ↔ boolvar)

Rule argument

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

Additional information

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