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Proof step 20 from proof mod-pot-shift-pos (previous step)

0 < j, ∀ i1, j, i. i→n(i1) < i→n(0 + 1) → 0 < j ∧ 0 < i1 → i1 = 0 ∨ (i % j) ^ i1 % j = i ^ i1 % j ⊦ 0 = j, (1 % j * i % j) % j = i % j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: one-03 seq: ⊦ 1 < j → 1 % j = 1 subst: [j] → [j] flags: rewrite

Additional information

Used simplifier rules: one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%modmod: j ≠ 0 ⊦ (i % j) % j = i % j; from specification int-div%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%one-01: ⊦ i = 1 → j % i = 0; from specification int-div%mod-zero-04: j ≠ 0 ⊦ 0 % j = 0; from specification int-div Used terms: j