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Proof step 8 from proof ushort-short (previous step)

us2i(sho) % 65536 < us2i(sho), 0 < us2i(sho), us2i(sho) % 65536 ≤ 32767, ~32768 ≤ us2i(sho), 32767 < us2i(sho) ⊦ i2s(us2i(sho)) = sho

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ abs(i) < j → i % j = i

Rule argument

seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [65536, us2i(sho)] rotate: F spec: int-div inst: name: mod-zero-05

Additional information

Used simplifier rules: ushort-max: ⊦ ¬ 65536 ≤ us2i(sho);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < j → abs(j) = j;%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0);% ⊦ ¬ i < i; Used terms: 65536, us2i(sho)