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Proof step 30 from proof shiftzero-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
# int2bits(i) < i→n(j), 0 ≤ i, # int2bits(i) < n ⊦ j = 0, bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + int2bits(i))) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n;% ⊦ bits2int(mklist(false, # int2bits(i))) = 0;