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Proof step 47 from proof bor-2pot-plus (previous step)

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)) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j, bitsinvert(int2bits(j0)).first, # int2bits(j0) ≤ i→n(i) ⊦ bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2int(uint2bits(j) + bitsinvert(bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i))))) = j * 2 ^ i + j0

Rule argument

Additional information

Used simplifier rules: ⊦ # mklist(boolvar, n) = n;% ⊦ # bitsinvert(bits) = # bits;% ⊦ int2bits(j) ≠ [];% ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bitsinvert(bitsinvert(bits)) = bits;% ⊦ bitsinvert(bits + bits0) = bitsinvert(bits) + bitsinvert(bits0);