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Proof step 10 from proof bor-2pot-plus (previous step)

¬(0 ≤ i ∧ 0 < j), j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j ⊦ bits2int(bitsinvert(bitsand(bitsinvert(uint2bits(j * 2 ^ i)), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
0 < 2 ^ i, 0 ≤ j0, 0 ≤ i, j0 < 2 ^ i ⊦ bits2int(bitsinvert(bitsand(true ', bitsinvert(int2bits(j0))))) = j0

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;% ⊦ bitsinvert(false ') = true ';% ⊦ uint2bits(0) = false ';% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * 0 = 0;% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;