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Proof step 108 from proof cast-mod-neg-high (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 109:
i→n(i) = # int2bits(j % 2 ^ i).rest, j % 2 ^ i < ~1, i→n(i) < # int2bits(j % 2 ^ i), j + 2 ^ i < i, j + 2 ^ i ≤ 0, j < j % 2 ^ i, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < 0, 0 < i, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, j % 2 ^ i < 0 ⊦ j = ~1, i = 1, j % 2 ^ i = 0, 2 ^ (n→i(# int2bits(j % 2 ^ i)) - 1) = 0

Rule argument

Additional information

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