simp
case b1
F : Type u_1
a b : F
inst✝ : CommRing F
z w : F
⊢ { b1 := z - w, b2 := 0 }.b1 = ({ b1 := z, b2 := 0 } - { b1 := w, b2 := 0 }).b1

case b2
F : Type u_1
a b : F
inst✝ : CommRing F
z w : F
⊢ { b1 := z - w, b2 := 0 }.b2 = ({ b1 := z, b2 := 0 } - { b1 := w, b2 := 0 }).b2
case b2
F : Type u_1
a b : F
inst✝ : CommRing F
z w : F
⊢ { b1 := z - w, b2 := 0 }.b2 = ({ b1 := z, b2 := 0 } - { b1 := w, b2 := 0 }).b2