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Proof step 24 from proof coprimes-min (previous step)

0 < i, min(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) ≤ 0, min(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) < i, ∀ i0. i0 ∈ filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i)) → min(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) ≤ i0 ⊦ filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i)) ≠ [], min(filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i))) = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
filterFun(λ j. gcd(i, j) = 1, count-i2j(1, i)) = [], 0 < i ⊦

Rule argument

Additional information

Used simplifier rules: min-empty: ⊦ min([]) = 0;%in-empty: ⊦ ¬ i ∈ []; from specification list[intlista]%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs