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

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

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
⊦ filterFun(intboolfun, ints) ≠ [] → max(filterFun(intboolfun, ints)) ≤ max(ints)
Proof step 6:
filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i)) ≠ [] → max(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) ≤ max(count-i2j(1, i)), 0 < i, 1 < i, i ≤ max(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))), 1 < max(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))), 0 < max(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) ⊦

Rule argument

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

Additional information

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