intros is_zero
n : ℕ
ord : Type
inst✝ : MonomialOrder (Variables n ord)
p : Polynomial n ord
dividers : List (Polynomial n ord)
dividers_non_empty : ¬(dividers == []) = true
not_div_by_zero : ¬(List.any dividers fun p => p == 0) = true
div_res : DivisionResult p dividers
h : div_res = divide_many p dividers dividers_non_empty not_div_by_zero
⊢ div_res.r = 0 → p ∈ asIdeal dividers
n : ℕ
ord : Type
inst✝ : MonomialOrder (Variables n ord)
p : Polynomial n ord
dividers : List (Polynomial n ord)
dividers_non_empty : ¬(dividers == []) = true
not_div_by_zero : ¬(List.any dividers fun p => p == 0) = true
div_res : DivisionResult p dividers
h : div_res = divide_many p dividers dividers_non_empty not_div_by_zero
is_zero : div_res.r = 0
⊢ p ∈ asIdeal dividers