simp only [take_cons_succ] at hps
case cons.succ
t : Prop
l : List Prop
ih : ∀ {ps : List Prop} {i j : Nat}, orN ps → ps = drop i (take j l) → orN l
ps : List Prop
i : Nat
hp : orN ps
j : Nat
hps : ps = drop i (take (j + 1) (t :: l))
⊢ t ∨ orN l
case cons.succ
t : Prop
l : List Prop
ih : ∀ {ps : List Prop} {i j : Nat}, orN ps → ps = drop i (take j l) → orN l
ps : List Prop
i : Nat
hp : orN ps
j : Nat
hps : ps = drop i (t :: take j l)
⊢ t ∨ orN l