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Proof step 4 from proof coprimes-prime (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i ≤ j → count-i2j(i, j) = count-i2j(i, j - 1) + j
Proof step 6:
1 ≤ i, prime(i) ⊦ filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i - 1) + i) = count-i2j(1, i - 1)

Rule argument

spec: inst: name: counti2j-rec seq: ⊦ i ≤ j → count-i2j(i, j) = count-i2j(i, j - 1) + j subst: [j, i] → [i, 1] flags: rewrite, current

Additional information

Used simplifier rules: leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd Used terms: i, 1