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Proof step 5 from proof div-div-01 (previous step)

i * i0 | i, 0 < i, 0 ≤ i0 ⊦ i = 0, i0 = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [i, i * i0] flags: rewrite, current

Additional information

Used simplifier rules: eq-same-02: ⊦ 0 < i → (i * j = i ↔ j = 1); from specification int-mult%eq-one: ⊦ i * j = 1 ↔ abs(i) = 1 ∧ i = j; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs Used terms: i, i * i0