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Proof step 89 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) ⊦ # int2bits(i) = i→n(j), bits2int(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), mklist(false, n - # int2bits(i)) + firstn(# int2bits(i) - i→n(j), int2bits(i)) = [], firstn(# int2bits(i) - i→n(j), int2bits(i)).first, (mklist(false, n - # int2bits(i)) + firstn(# int2bits(i) - i→n(j), int2bits(i))).first

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] ∧ (bits.first ↔ boolvar) → bits2int(mklist(boolvar, n) + bits) = bits2int(bits) subst: [bits, n, boolvar] → [firstn(# int2bits(i) - i→n(j), int2bits(i)), n - # int2bits(i), false] rotate: F spec: int2bits inst: name: bits2int-mklist

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ firstn(n, bits) = [] ↔ n = 0;% ⊦ n < m → m - n ≠ 0; Used terms: firstn(# int2bits(i) - i→n(j), int2bits(i)), n - # int2bits(i), false