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Proof step 17 from proof coprimes-prime (previous step)

prime(i), i0 < i, 0 < i0, 1 < i, 0 < i ⊦ i = 1, filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i - 1)) = count-i2j(1, i - 1), gcd(i0, i) = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ prime(j) ∧ 1 < i ∧ i < j → gcd(i, j) = 1

Rule argument

spec: int-gcd inst: name: gcd-prime seq: ⊦ prime(j) ∧ 1 < i ∧ i < j → gcd(i, j) = 1 subst: [j, i] → [i, i0] flags: rewrite

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%gcd-one-01: ⊦ gcd(i, 1) = 1; from specification int-gcd%gcd-com: ⊦ gcd(i, j) = gcd(j, i); from specification int-gcd Used terms: i, i0