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Proof step 9 from proof cast-mod-ls-neg (previous step)

¬ j < ~1, i→n(i) < # int2bits(j), 0 < 2 ^ (i - 1) + j, j < 0, 0 < i ⊦ bits2int(lastn(i→n(i), int2bits(j))) = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
0 < i, 1 < i, i→n(i) < # int2bits(~1) ⊦ bits2int(lastn(i→n(i), int2bits(~1))) = ~1

Rule argument

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ 1 < 2 ^ i ↔ 0 < i;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ ¬ i < j ↔ j ≤ i;