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Proof step 7 from proof coprimes-max (previous step)

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))) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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)) ⊦

Rule argument

Additional information

Used simplifier rules: forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs