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Proof step 3 from proof sis-ls-same (previous step)

i < 0 ⊦ i < s2i(i2s(i)) ↔ ¬ ~32768 ≤ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ i < 0 ∧ ~32768 ≤ i % 65536 → s2i(i2s(i)) = i % 65536
Proof step 5:
¬(i < 0 ∧ ~32768 ≤ i % 65536), i < 0 ⊦ i < s2i(i2s(i)) ↔ ¬ ~32768 ≤ i
Proof step 8:
i < 0 ∧ ~32768 ≤ i % 65536, i < 0 ⊦ i < i % 65536 ↔ ¬ ~32768 ≤ i

Rule argument

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

Additional information

Used terms: i