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Proof step 7 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 ⊦ # sgn(bitsinvert(uint2bits(~ j)) +1) = i→n(i + 2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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 ⊦ # sgn(bitsinvert(uint2bits(~ j)) +1) = i→n(i + 2), true ∈ uint2bits(~ j).rest.rest

Rule argument

Additional information

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