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Proof step 46 from proof cast-mod-neg-high (previous step)

j ≤ ~(2 ^ i) ∧ 0 < i ∧ j % 2 ^ i = 0, j % 2 ^ i = 0, 0 ≤ 2 ^ (i - 1), j + 2 ^ i ≤ 0, j + 2 ^ i < i, i→n(i) ≤ #(int2bits(j / 2 ^ i) + fillsgn(i→n(i + 1), int2bits(j % 2 ^ i)).rest), 2 ^ (i - 1) + j < 0, 0 < i, j < 0 ⊦ i = 1, j = ~1, bits2int(lastn(i→n(i), int2bits(j / 2 ^ i) + fillsgn(i→n(i + 1), int2bits(j % 2 ^ i)).rest)) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
j % 2 ^ i = 0, j + 2 ^ i < i, j + 2 ^ i ≤ 0, 0 ≤ 2 ^ (i - 1), j < 0, 0 < i, 2 ^ (i - 1) + j < 0 ⊦ j = ~1, i = 1, bits2int(mklist(false, i→n(i))) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n;% ⊦ # mklist(boolvar, n) = n;% ⊦ lastn(n, bits + mklist(boolvar, n)) = mklist(boolvar, n);% ⊦ (boolvar ' + bits).rest = bits;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ bits + [] = bits;% ⊦ mklist(boolvar, 0) = [];%n ≠ 0 ⊦ mklist(false, (* n)) = false ' + mklist(false, n -1);% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ fillsgn(n + 1, boolvar ') = mklist(boolvar, n + 1);% ⊦ int2bits(0) = false ';% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 < i → i→n(i + 1) = i→n(i) + 1;