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Proof step 17 from proof max_exp-fac-add (previous step)

0 < Π countFun(1, j0, λ j0. i * j + j0), 0 < fac(i * j), i | j1, j1 ∈ countFun(1, j0, λ j0. i * j + j0), 0 ≤ j, 0 < i, 0 ≤ j0, 0 < j, j0 < i, prime(i) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: intlist inst: name: countFun-in seq: ⊦ i0 ∈ countFun(i, j, intfun) ↔ (∃ j0. i ≤ j0 ∧ j0 ≤ j ∧ intfun(j0) = i0) subst: [intfun, j, i, i0] → [λ j0. i * j + j0, j0, 1, j1] flags: rewrite

Additional information

Used simplifier rules: divides-mult-add: ⊦ i | i * j + j0 ↔ i | j0; from specification int-gcd%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%div-not-ls: ⊦ i < j ∧ 0 < i → ¬ j | i; from specification int-gcd Used terms: λ j0. i * j + j0, j0, 1, j1