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Proof step 27 from proof bor-2pot-plus (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
int2bits(j0) = boolvar + bits ∧ int2bits(j0) ≠ [], # int2bits(j0) = i→n(i) + 1, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ 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

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [int2bits(j0), boolvar, bits] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: int2bits(j0), boolvar, bits