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Proof step 8 from proof fermat-2-mod (previous step)

gcd(j, i) = 1, i ^ (j - 1) |%| j = 1 |%| j, prime(j), 0 < j ⊦ 1 |%| j = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 ≤ i ∧ i < j → i |%| j = i

Rule argument

spec: int-mod inst: name: mod-zero seq: ⊦ 0 ≤ i ∧ i < j → i |%| j = i subst: [j, i] → [j, 1] flags: rewrite, current

Additional information

Used simplifier rules: mod-one: ⊦ i |%| 1 = 0;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%sub-eq-01: ⊦ i = j → i - j = 0; from specification int-abs%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%gcd-one-01: ⊦ gcd(i, 1) = 1; from specification int-gcd%gcd-com: ⊦ gcd(i, j) = gcd(j, i); from specification int-gcd%prime-one: ⊦ i ≤ 1 → ¬ prime(i); from specification int-gcd Used terms: j, 1