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Proof step 50 from proof bor-2pot-plus-01 (previous step)

0 < j0, # 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, i→n(i) ≤ # int2bits(j0).rest ⊦ i = 0, bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], (j + 1) * 2 ^ n→i(# int2bits(j0).rest) = (j * 2 ^ i + j0) + (2 ^ (n→i(# uint2bits(j0)) - 1) - j0 + 1) + 1, int2bits(j0).rest = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
# int2bits(j0) = i→n(i) + 1, 0 ≤ 2 ^ i, 0 < 2 ^ i, j + 1 < j0, 0 < j0, j < 0, j + 1 < i, 0 ≤ j0, j < i, j < j0, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j < 2 ^ i, j0 < 2 ^ i, 0 < i, i→n(i) ≤ # int2bits(j0).rest, 1 < 2 ^ i, 2 + j < 2 ^ i ⊦ int2bits(j0).rest = [], i = 0, bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], (j + 1) * 2 ^ n→i(# int2bits(j0).rest) = 2 ^ (n→i(# uint2bits(j0)) - 1) + j * 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i + j < i0 ∧ ¬ j < j0 → i + j0 < i0;% ⊦ (* i) < j ∧ 0 < i → 0 ≤ j ∧ 0 < j; (forward)% ⊦ i < j ∧ j < j0 → i < j0; (forward)% ⊦ i +1 = i + 1;% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + (j - i) = j;