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Proof step 6 from proof modmod-add-01 (previous step)

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

User applied rule insert 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: [j, i, i0] → [~ j, i, i0]

Additional information

Used simplifier rules: mod-neg: j ≠ 0 ⊦ i % ~ j = i % j;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ 0 < ~ i ↔ i < 0; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: ~ j, i, i0