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Proof step 8 from proof ushort-pos-01 (previous step)

0 < i, 32767 < i, 0 ≤ s2i(i2s(i)), 0 ≤ i, i < 65536 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 ≤ i ∧ 32767 < i % 65536 → s2i(i2s(i)) = i % 65536 - 65536

Rule argument

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

Additional information

Used simplifier rules: ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;%0 < j ⊦ 0 ≤ i ∧ i < j → i % (* j) = i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i