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Proof step 30 from proof int2bits-len-neg (previous step)

0 < ~ j ∧ true ∈ uint2bits(~ j).rest.rest, j < 2 ^ i, j < 0, j < ~1, j + 2 ^ i < i, j + 2 ^ i < 0, 0 ≤ 2 ^ i * 2 + j, 0 ≤ i, 0 < 2 ^ i, j < i, j + 1 < 2 ^ i ⊦ # bitsinvert(uint2bits(~ j)) +1 = i→n(i + 2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
true ∈ uint2bits(~ j).rest.rest, j < 2 ^ i, j < ~1, j + 2 ^ i < i, j + 2 ^ i < 0, 0 ≤ 2 ^ i * 2 + j, 0 ≤ i, 0 < 2 ^ i, j < i, j + 1 < 2 ^ i, j < 0 ⊦ # bitsinvert(uint2bits(~ j)) +1 = i→n(i + 2)

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 < ~ i ↔ i < 0;