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Proof step 8 from proof coprimes-max (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i ≤ j → max(count-i2j(i, j)) = j
Proof step 10:
1 ≤ i, 0 < max(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))), i ≤ i, 1 < max(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))), i ≤ max(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))), 1 < i, 0 < i, max(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) ≤ i, 1 < i, 0 < i ⊦

Rule argument

spec: inst: name: count-i2j-max seq: ⊦ i ≤ j → max(count-i2j(i, j)) = 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%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: i, 1