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Proof step 20 from proof ushort-pos-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ i < 0 ∧ i % 65536 < ~32768 → s2i(i2s(i)) = i % 65536 + 65536
Proof step 22:
¬(i < 0 ∧ i % 65536 < ~32768), ~65536 ≤ i, i < 0, s2i(i2s(i)) < 0, i < ~32768 ⊦ s2i(i2s(i)) = i

Rule argument

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

Additional information

Used simplifier rules: ⊦ 0 < j → ¬ j + i % j < 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i