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Proof step 7 from proof shiftzero-rec-neg-shorter (previous step)

i < ~1, # int2bits(i) ≤ n, i < 0, 1 < j, 0 < j ⊦ bits2int(sublist(0, # fillsgn(n, int2bits(i)), mklist(false, i→n(j)) + fillsgn(n, int2bits(i)))) = bits2int(sublist(0, # fillsgn(n - 1, int2bits((i - 1) / 2)), mklist(false, i→n(j) - 1) + fillsgn(n - 1, int2bits((i - 1) / 2))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
i < ~1, # int2bits(i) ≤ n, i < 0, 1 < j, 0 < j ⊦ bits2int(sublist(0, n, mklist(false, i→n(j)) + fillsgn(n, int2bits(i)))) = bits2int(sublist(0, # fillsgn(n - 1, int2bits((i - 1) / 2)), mklist(false, i→n(j) - 1) + fillsgn(n - 1, int2bits((i - 1) / 2))))

Rule argument

Additional information

Used simplifier rules: ⊦ # bits ≤ n → # fillsgn(n, bits) = n;