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Proof step 14 from proof sis-neg-high (previous step)

¬(i0 < 0 ∧ j < 0 ∧ abs(j) < 2 ^ (16 - 1) ∧ 0 < 16), # int2bits(j) ≤ 16, abs(j) < 2 ^ 16, ~32768 ≤ j, i0 * 2 ^ 16 + j < ~32768, j ≤ 0, i0 ≤ 0, i0 * 2 ^ 16 + j < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 * 2 ^ 16 + j))))) = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < i ∧ j < 0 → ((* i) * i0 < (* j) ↔ i0 < j / i);% ⊦ # boolvar ' = 0 +1;% ⊦ int2bits(0) = false ';% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i + 0 = i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;