induction δ generalizing v w
W : Type
M : KripkeModel W
δ : List Program
v w : W
⊢ relateSeq M δ v w → δ ≠ [] → ∃ l, l.length + 1 = δ.length ∧ List.Chain' (pairRel M) (((?'⊤) :: δ).zip (v :: l ++ [w]))
case nil
W : Type
M : KripkeModel W
v w : W
⊢ relateSeq M [] v w → [] ≠ [] → ∃ l, l.length + 1 = [].length ∧ List.Chain' (pairRel M) ([?'⊤].zip (v :: l ++ [w]))

case cons
W : Type
M : KripkeModel W
head✝ : Program
tail✝ : List Program
tail_ih✝ :
  ∀ {v w : W},
    relateSeq M tail✝ v w →
      tail✝ ≠ [] → ∃ l, l.length + 1 = tail✝.length ∧ List.Chain' (pairRel M) (((?'⊤) :: tail✝).zip (v :: l ++ [w]))
v w : W
⊢ relateSeq M (head✝ :: tail✝) v w →
    head✝ :: tail✝ ≠ [] →
      ∃ l,
        l.length + 1 = (head✝ :: tail✝).length ∧ List.Chain' (pairRel M) (((?'⊤) :: head✝ :: tail✝).zip (v :: l ++ [w]))