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Proof step 3 from proof modmod-add-if (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: modmod-add seq: 0 < j ⊦ 0 ≤ i ∧ 0 ≤ i0 → (i % j + i0) % j = (i + i0) % j subst: [i0, j, i] → [i, j, i0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i, j, i0