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Proof step 8 from proof mod-nls-04 (previous step)

0 < j, abs(i % j) < j, i % j < i0, i0 < 0, i0 + j ≤ 1 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i ≠ j → (i ≤ j ↔ i ≤ j - 1)
Proof step 10:
i0 + j = 1, i0 < 0, i % j < i0, abs(i % j) < j, 0 < j, i0 + j ≤ 1 ⊦
Proof step 12:
i0 < 0, i % j < i0, abs(i % j) < j, 0 < j, i0 + j ≤ 1 - 1 ⊦ i0 + j = 1

Rule argument

spec: int-abs name: le-rec seq: ⊦ i ≠ j → (i ≤ j ↔ i ≤ j - 1) subst: [j, i] → [1, i0 + j] flags: <all paths>

Additional information

Used terms: 1, i0 + j