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Proof step 5 from proof bor-2pot-plus (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → int2bits(i) = uint2bits(i) subst: [i] → [j * 2 ^ i] rotate: F spec: int2bits inst: name: int2bits-pos

Additional information

Used simplifier rules: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: j * 2 ^ i