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Proof step 41 from proof bor-2pot-plus-01 (previous step)

¬(¬ false ∈ mklist(true, i→n(i)) ∧ # mklist(true, i→n(i)) ≤ # bitsinvert(int2bits(j0).rest) ∧ mklist(true, i→n(i)) ≠ []), # 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)) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
# int2bits(j0) = i→n(i) + 1, # int2bits(j0).rest < i→n(i), 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 ⊦ bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], i = 0, bits2int(int2bits(j) + bitsinvert(bitsand(bitsinvert(int2bits(j0).rest), mklist(true, i→n(i))))) = j * 2 ^ i + j0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (forward)% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ # bitsinvert(bits) = # bits;% ⊦ # mklist(boolvar, n) = n;% ⊦ ¬ false ∈ mklist(true, n);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;