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Proof step 45 from proof int2bits-rec-2pot-neg-02 (previous step)

¬ 0 < ~(j / 2 ^ i), j / 2 ^ i < i, j / 2 ^ i ≤ 0, 0 < i, j + 2 ^ i ≤ 0, j + 2 ^ i < i, j < 0, 0 ≤ i, true ∈ fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest ⊦ sgn(bitsinvert(uint2bits(~(j / 2 ^ i))) + bitsinvert(fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest) +1) = sgn(bitsinvert(uint2bits(1 - j / 2 ^ i)) +1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j % 2 ^ i = 0, false ∈ uint2bits(~(j / 2 ^ i)) ∧ true ∈ uint2bits(~(j / 2 ^ i))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
j / 2 ^ i = 0, true ∈ fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest, 0 ≤ i, j < 0, j + 2 ^ i < i, j + 2 ^ i ≤ 0, 0 < i ⊦ j % 2 ^ i = 0, sgn(true ' + bitsinvert(fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest) +1) = true ' + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest

Rule argument

Additional information

Used simplifier rules: uint2bits-zero: ⊦ uint2bits(0) = false ';%uint2bits-one: ⊦ uint2bits(1) = false + true;% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ sgn(true ' + true ') = true ';% ⊦ bits + boolvar = bits + boolvar ';% ⊦ (bits + false ')+1 = bits + true;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ bitsinvert(true ') = false ';% ⊦ bitsinvert(false ' + bits) = true + bitsinvert(bits);% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ bitsinvert(false ') = true ';% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < ~ i ↔ i < 0;