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Proof step 18 from proof coprimes-min (previous step)

0 < i, ∀ i0. i0 ∈ filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i)) → min(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) ≤ i0 ⊦ 1 ∈ filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i)), min(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: count-i2j-in: ⊦ i0 ∈ count-i2j(i, j) ↔ i ≤ i0 ∧ i0 ≤ j;%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%gcd-one-01: ⊦ gcd(i, 1) = 1; from specification int-gcd Used terms: count-i2j(1, i), λ j. gcd(i, j) = 1, 1