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Proof step 2 from proof sis-neg-lower (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i < 0 ∧ i % 65536 < ~32768 → s2i(i2s(i)) = i % 65536 + 65536
Proof step 4:
¬(i < 0 ∧ i % 65536 < ~32768), i < ~32768, ~65536 < i, i < 0 ⊦ s2i(i2s(i)) = i + 65536
Proof step 7:
i < 0 ∧ i % 65536 < ~32768, i < ~32768, ~65536 < i, i < 0 ⊦ i % 65536 + 65536 = i + 65536

Rule argument

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

Additional information

Used terms: i