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Proof step 10 from proof ushort-pos-02 (previous step)

¬(i < 0 ∧ ~32768 ≤ i % 65536), 0 ≤ s2i(i2s(i)), i < 0, ~65536 ≤ i, i < ~32768 ⊦ s2i(i2s(i)) = i + 65536

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
~65536 ≤ i % 65536, i % 65536 < ~32768, i < ~32768, ~65536 ≤ i, i < 0 ⊦ i % 65536 = i, i % 65536 = 0

Rule argument

Additional information

Used simplifier rules: sis-neg-low: ⊦ i < 0 ∧ i % 65536 < ~32768 → s2i(i2s(i)) = i % 65536 + 65536;% ⊦ i < 0 ∧ 0 ≤ j → i < j;%0 < j ⊦ i % (* j) < 0 ↔ i < 0 ∧ i % j ≠ 0;% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;