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Proof step 17 from proof bor-2pot-plus (previous step)

0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j ⊦ bits2int(bitsinvert(bitsand(bitsinvert(int2bits(j0)), bitsinvert(uint2bits(j)) + mklist(true, i→n(i))))) = j * 2 ^ i + j0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ bits.first ∧ # bits ≤ # bits1 ∧ bits ≠ [] → bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits, bits1)
Proof step 19:
¬(bitsinvert(int2bits(j0)).first ∧ # bitsinvert(int2bits(j0)) ≤ # mklist(true, i→n(i)) ∧ bitsinvert(int2bits(j0)) ≠ []), 0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j ⊦ bits2int(bitsinvert(bitsand(bitsinvert(int2bits(j0)), bitsinvert(uint2bits(j)) + mklist(true, i→n(i))))) = j * 2 ^ i + j0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = []
Proof step 47:
bitsinvert(int2bits(j0)).first ∧ # bitsinvert(int2bits(j0)) ≤ # mklist(true, i→n(i)) ∧ bitsinvert(int2bits(j0)) ≠ [], 0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j ⊦ bits2int(bitsinvert(bitsinvert(uint2bits(j)) + bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i))))) = j * 2 ^ i + j0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = []

Rule argument

name: and-size-one rotate: F subst: [bits1, bits0, bits] → [mklist(true, i→n(i)), bitsinvert(uint2bits(j)), bitsinvert(int2bits(j0))]

Additional information

Used terms: mklist(true, i→n(i)), bitsinvert(uint2bits(j)), bitsinvert(int2bits(j0))