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Proof step 2 from proof bor-2pot-plus-01 (previous step)

j < 2 ^ i, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, j < 0, 0 < 2 ^ i, j < i, j < j0, j + 1 < 2 ^ i ⊦ bits2int(bitsor(int2bits(j * 2 ^ i), int2bits(j0))) = j * 2 ^ i + j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsor(bits, bits0) = bitsinvert(bitsand(bitsinvert(bits), bitsinvert(bits0)))
Proof step 4:
int2bits(j * 2 ^ i) ≠ [] ∧ int2bits(j0) ≠ [], j < 2 ^ i, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, j < 0, 0 < 2 ^ i, j < i, j < j0, j + 1 < 2 ^ i ⊦ bits2int(bitsinvert(bitsand(bitsinvert(int2bits(j * 2 ^ i)), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0

Rule argument

name: or-invandinv rotate: F subst: [bits0, bits] → [int2bits(j0), int2bits(j * 2 ^ i)]

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(j0), int2bits(j * 2 ^ i)