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Proof step 12 from proof cast-mod-ls-neg (previous step)

# int2bits(j) ≤ i→n(i) ∧ int2bits(j) ≠ [], 0 < i, j < 0, 0 < 2 ^ (i - 1) + j ⊦ bits2int(lastn(i→n(i), mklist(int2bits(j).first, i→n(i) - # int2bits(j)) + int2bits(j))) = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# int2bits(j) ≤ i→n(i), 0 < i, j < 0, 0 < 2 ^ (i - 1) + j ⊦ bits2int(lastn(i→n(i), mklist(true, i→n(i) - # int2bits(j)) + int2bits(j))) = j

Rule argument

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];% ⊦ j < 0 → int2bits(j).first;