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Proof step 22 from proof ushort-pos-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
i < ~32768, ~32768 ≤ i % 65536, ~65536 ≤ i, i < 0, i < i % 65536 ⊦ i % 65536 = i, i % 65536 = 0

Rule argument

Additional information

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