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Proof step 5 from proof modmod-add-law (previous step)

⊦ (i % j + i0 % j) % j = (i + i0) % j - j, (i % j + i0 % j) % j = (i + i0) % j + j, (i % j + i0 % j) % j = (i + i0) % j, 0 = j, j < 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: modmod-add-law-pos seq: 0 < j ⊦ (i % j + i0 % j) % j = (i + i0) % j ∨ (i % j + i0 % j) % j = (i + i0) % j + j ∨ (i % j + i0 % j) % j = (i + i0) % j - j subst: [j, i, i0] → [j, i, i0]

Additional information

Used simplifier rules: ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss) Used terms: j, i, i0