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Proof step 15 from proof coprimes-max (previous step)

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

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, i] flags: rewrite, current

Additional information

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