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Proof step 12 from proof coprimes-prime (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
∀ i. i ∈ ints → intboolfun(i) ⊦ filterFun(intboolfun, ints) = ints
Proof step 14:
¬(∀ i0. i0 ∈ count-i2j(1, i - 1) → gcd(i, i0) = 1), prime(i), 0 < i ⊦ i = 1, filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i - 1)) = count-i2j(1, i - 1)

Rule argument

spec: inst: name: filterFun-all seq: ∀ i. i ∈ ints → intboolfun(i) ⊦ filterFun(intboolfun, ints) = ints subst: [ints, intboolfun] → [count-i2j(1, i - 1), λ j. gcd(i, j) = 1] flags: rewrite, current

Additional information

Used terms: count-i2j(1, i - 1), λ j. gcd(i, j) = 1