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Proof step 2 from proof sis-pos-low (previous step)

i % 65536 ≤ 32767, 0 ≤ i ⊦ s2i(i2s(i)) = i % 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
~32768 ≤ i, i ≤ 32767 ⊦ s2i(i2s((* i))) = i
Proof step 4:
¬(~32768 ≤ i ∧ i ≤ 32767), i % 65536 ≤ 32767, 0 ≤ i ⊦ s2i(i2s(i)) = i % 65536
Proof step 33:
~32768 ≤ i ∧ i ≤ 32767, i % 65536 ≤ 32767, 0 ≤ i ⊦ i = i % 65536

Rule argument

name: num-issi rotate: F subst: [i] → [i]

Additional information

Used terms: i