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Proof step 1 from proof bor-2pot-plus (conclusion)

⊦ j0 < 2 ^ i ∧ 0 ≤ i ∧ 0 ≤ j0 ∧ 0 ≤ j → bor(j * 2 ^ i, j0) = j * 2 ^ i + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 ≤ j, 0 < 2 ^ i ⊦ bits2int(bitsor(int2bits(j * 2 ^ i), int2bits(j0))) = j * 2 ^ i + j0

Rule argument

Additional information

Used simplifier rules: bor-def: ⊦ bor(i, j) = bits2int(bitsor(int2bits(i), int2bits(j)));% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)