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Proof step 33 from proof bor-2pot-plus-01 (previous step)

0 < i, j0 < 2 ^ i, j < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j + 1 < 2 ^ i, j < j0, j < i, 0 < 2 ^ i, 0 ≤ j0, j + 1 < i, j < 0 ⊦ i = 0, bits2int(bitsinvert(bitsand(bitsinvert(int2bits(j0)), bitsinvert(int2bits(j)) + mklist(true, i→n(i))))) = j * 2 ^ i + j0, bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ bits.first ∧ # bits ≤ # bits1 ∧ bits ≠ [] → bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits, bits1)
Proof step 35:
¬(bitsinvert(int2bits(j0)).first ∧ # bitsinvert(int2bits(j0)) ≤ # mklist(true, i→n(i)) ∧ bitsinvert(int2bits(j0)) ≠ []), 0 < i, j0 < 2 ^ i, j < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j + 1 < 2 ^ i, j < j0, j < i, 0 < 2 ^ i, 0 ≤ j0, j + 1 < i, j < 0 ⊦ i = 0, bits2int(bitsinvert(bitsand(bitsinvert(int2bits(j0)), bitsinvert(int2bits(j)) + mklist(true, i→n(i))))) = j * 2 ^ i + j0, bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = []
Proof step 56:
bitsinvert(int2bits(j0)).first ∧ # bitsinvert(int2bits(j0)) ≤ # mklist(true, i→n(i)) ∧ bitsinvert(int2bits(j0)) ≠ [], 0 < i, j0 < 2 ^ i, j < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j + 1 < 2 ^ i, j < j0, j < i, 0 < 2 ^ i, 0 ≤ j0, j + 1 < i, j < 0 ⊦ i = 0, bits2int(bitsinvert(bitsinvert(int2bits(j)) + bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i))))) = j * 2 ^ i + j0, bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = []

Rule argument

name: and-size-one rotate: F subst: [bits1, bits0, bits] → [mklist(true, i→n(i)), bitsinvert(int2bits(j)), bitsinvert(int2bits(j0))]

Additional information

Used terms: mklist(true, i→n(i)), bitsinvert(int2bits(j)), bitsinvert(int2bits(j0))