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Proof step 79 from proof bor-2pot-plus-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
i→n(i) = n + # int2bits(j0), 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, # int2bits(j0) < i→n(i) ⊦ mklist(true, n) + bitsinvert(int2bits(j0)) = [], bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], i = 0, (j + 1) * 2 ^ n→i(n) * 2 ^ n→i(# int2bits(j0)) = j * 2 ^ i + 2 ^ n→i(n) * 2 ^ n→i(# int2bits(j0)), i→n(i) = # int2bits(j0), n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 ≤ n→i(n);