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Proof step 26 from proof bor-2pot-plus (previous step)

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)) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
# 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

Rule argument

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ 0 ≤ j → bitsinvert(int2bits(j)).first;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;%0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bitsinvert(bitsinvert(bits)) = bits;% ⊦ bitsinvert(bits + bits0) = bitsinvert(bits) + bitsinvert(bits0);%bits ≠ [] ⊦ bitsinvert(bits).rest = bitsinvert(bits.rest);% ⊦ int2bits(j) ≠ [];% ⊦ # mklist(boolvar, n) = n;% ⊦ # bitsinvert(bits) = # bits;% ⊦ m + n = n + m;