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Proof step 15 from proof sis-ls-same (previous step)

i % 65536 ≤ 32767, i < i % 65536, 0 ≤ i, i < 32767, 0 < i % 65536 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ abs(i) < j → i % j = i

Rule argument

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

Additional information

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