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Proof step 8 from proof ushort-pos-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i < 0 ∧ ~32768 ≤ i % 65536 → s2i(i2s(i)) = i % 65536
Proof step 10:
¬(i < 0 ∧ ~32768 ≤ i % 65536), 0 ≤ s2i(i2s(i)), i < 0, ~65536 ≤ i, i < ~32768 ⊦ s2i(i2s(i)) = i + 65536
Proof step 13:
i < 0 ∧ ~32768 ≤ i % 65536, 0 ≤ i % 65536, i < 0, ~65536 ≤ i, i < ~32768 ⊦ i % 65536 = i + 65536

Rule argument

name: sis-neg-high rotate: F subst: [i] → [i]

Additional information

Used terms: i