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Proof step 82 from proof shiftzero-pos (previous step)

# int2bits(i) ≤ n, 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, 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 83:
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, 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

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m < n → m ≤ n;