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Proof step 20 from proof bor-2pot-plus (previous step)

# int2bits(j0) = i→n(i) + 1, 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 21:
⊦ bits.first ∧ # bits = # bits1 + 1 ∧ bits1 ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits.rest, bits1)
Proof step 22:
¬ (bitsinvert(int2bits(j0)).first ∧ # bitsinvert(int2bits(j0)) = # mklist(true, i→n(i)) + 1 ∧ mklist(true, i→n(i)) ≠ [] ∧ bitsinvert(uint2bits(j)) ≠ []), # int2bits(j0) = i→n(i) + 1, 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 26:
bitsinvert(int2bits(j0)).first ∧ # bitsinvert(int2bits(j0)) = # mklist(true, i→n(i)) + 1 ∧ mklist(true, i→n(i)) ≠ [] ∧ bitsinvert(uint2bits(j)) ≠ [], # int2bits(j0) = i→n(i) + 1, 0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j ⊦ bits2int(bitsinvert(bitsinvert(uint2bits(j)) + bitsand(bitsinvert(int2bits(j0)).rest, mklist(true, i→n(i))))) = j * 2 ^ i + j0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = []

Rule argument

name: and-size-one-01 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))