α : Type u_1
inst✝ : NonUnitalNonAssocRing α
k : α
h : ∀ (x : α), x * k = 0 → x = 0
x y : α
h' : x * k = y * k
⊢ (x - y) * k = 0
α : Type u_1
inst✝ : NonUnitalNonAssocRing α
k : α
h : ∀ (x : α), x * k = 0 → x = 0
⊢ IsRightRegular k
refine' fun x y (h' : x * k = y * k) => sub_eq_zero.mp (h _ _)
no goals
α : Type u_1
inst✝ : NonUnitalNonAssocRing α
k : α
h : ∀ (x : α), x * k = 0 → x = 0
x y : α
h' : x * k = y * k
⊢ (x - y) * k = 0
rw [sub_mul, sub_eq_zero, h']