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Proof step 29 from proof bor-2pot-plus (previous step)

# int2bits(j0) = i→n(i) + 1, int2bits(j0) = boolvar ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, boolvar ∈ int2bits(j0) ⊦ i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2int(uint2bits(j) + bitsinvert(bitsand(bitsinvert(bits), mklist(true, i→n(i))))) = j * 2 ^ i + j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ ¬ false ∈ bits ∧ # bits ≤ # bits0 ∧ bits ≠ [] → bitsand(bits0, bits) = bits0
Proof step 31:
¬(¬ false ∈ mklist(true, i→n(i)) ∧ # mklist(true, i→n(i)) ≤ # bitsinvert(bits) ∧ mklist(true, i→n(i)) ≠ []), # int2bits(j0) = i→n(i) + 1, int2bits(j0) = boolvar ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, boolvar ∈ int2bits(j0) ⊦ i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2int(uint2bits(j) + bitsinvert(bitsand(bitsinvert(bits), mklist(true, i→n(i))))) = j * 2 ^ i + j0
Proof step 33:
¬ false ∈ mklist(true, i→n(i)) ∧ # mklist(true, i→n(i)) ≤ # bitsinvert(bits) ∧ mklist(true, i→n(i)) ≠ [], # int2bits(j0) = i→n(i) + 1, int2bits(j0) = boolvar ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, boolvar ∈ int2bits(j0) ⊦ i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2int(uint2bits(j) + bitsinvert(bitsinvert(bits))) = j * 2 ^ i + j0

Rule argument

name: add-ones-lelen-01 rotate: F subst: [bits, bits0] → [mklist(true, i→n(i)), bitsinvert(bits)]

Additional information

Used terms: mklist(true, i→n(i)), bitsinvert(bits)