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Proof step 38 from proof bor-2pot-plus-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
# int2bits(j0) = i→n(i) + 1, j < 0, j + 1 < i, 0 ≤ j0, 0 < 2 ^ i, j < i, j < j0, j + 1 < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j < 2 ^ i, j0 < 2 ^ i, 0 < i ⊦ bits2int(int2bits(j) + bitsinvert(bitsand(bitsinvert(int2bits(j0).rest), mklist(true, i→n(i))))) = j * 2 ^ i + j0, i = 0, bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = []

Rule argument

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 ≤ j → bitsinvert(int2bits(j)).first;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ 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;