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Proof step 15 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(i, i0) = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ gcd(i, j) = gcd(j, i)
Proof step 17:
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

Rule argument

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

Additional information

Used terms: i0, i