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Proof step 10 from proof max_exp-fac-add (previous step)

¬(∀ i0. i0 ∈ countFun(1, j0, λ j0. i * j + j0) → 0 < i0), Π countFun(1, j0, λ j0. i * j + j0) < fac(i * j), Π countFun(1, j0, λ j0. i * j + j0) < i, Π countFun(1, j0, λ j0. i * j + j0) < j, Π countFun(1, j0, λ j0. i * j + j0) ≤ 0, 0 < fac(i * j), 0 ≤ j, 0 < i, 0 ≤ j0, 0 < j, j0 < i, prime(i) ⊦ max_exp(i, fac(i * j) * Π countFun(1, j0, λ j0. i * j + j0)) = max_exp(i, fac(i * j))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
i0 < j, i0 < i, i0 < fac(i * j), i0 ≤ 0, prime(i), j0 < i, 0 < j, 0 ≤ j0, 0 < i, 0 ≤ j, 0 < fac(i * j), Π countFun(1, j0, λ j0. i * j + j0) ≤ 0, Π countFun(1, j0, λ j0. i * j + j0) < j, Π countFun(1, j0, λ j0. i * j + j0) < i, Π countFun(1, j0, λ j0. i * j + j0) < fac(i * j), i0 ∈ countFun(1, j0, λ j0. i * j + j0) ⊦ max_exp(i, fac(i * j) * Π countFun(1, j0, λ j0. i * j + j0)) = max_exp(i, fac(i * j))

Rule argument

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs