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Proof step 82 from proof cast-mod-neg-high (previous step)

~1 + 1 = 0, ~1 = j % 2 ^ i, i→n(i) = # fillsgn(i→n(i) + 1, true ').rest, # true ' ≤ i→n(i), j + 2 ^ i < i, j + 2 ^ i ≤ 0, j < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, j + 2 ^ i < 2 ^ (i - 1), 0 < i, j + 1 < 2 ^ (i - 1), j < ~1 ⊦ bits2int(fillsgn(i→n(i) + 1, true ').rest) = ~1, j = ~1, i = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 83:
~1 = j % 2 ^ i, j + 2 ^ i < i, j + 2 ^ i ≤ 0, j < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, j + 2 ^ i < 2 ^ (i - 1), j + 1 < 2 ^ (i - 1), j < ~1, 0 < i ⊦ j = ~1, i = 1, bits2int(mklist(true, i→n(i))) = ~1

Rule argument

Additional information

Used simplifier rules: ⊦ 1 ≤ i ↔ 0 < i;%0 ≤ i ⊦ (* m) ≤ i→n(i) ↔ n→i(m) ≤ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ # boolvar ' = 0 +1;% ⊦ i→n(i) = i→n(j) ↔ abs(i) = abs(j);% ⊦ # mklist(boolvar, n) = n;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + [] = bits;% ⊦ mklist(boolvar, 0) = [];%n ≠ 0 ⊦ mklist(true, (* n)) = true ' + mklist(true, n -1);% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ fillsgn(n + 1, boolvar ') = mklist(boolvar, n + 1);