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Proof step 33 from proof int2bits-len-neg (previous step)

false ∈ bitsinvert(uint2bits(~ j)), 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)) = i→n(i + 2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
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 ⊦ # uint2bits(~ j) = i→n(i + 2)

Rule argument

Additional information

Used simplifier rules: uint2bits-onein-01: ⊦ j < 0 → true ∈ uint2bits(~ j);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ false ∈ bitsinvert(bits) ↔ true ∈ bits;% ⊦ # bitsinvert(bits) = # bits;