| RAbsCo Γ Δ Σ κ σ σ₁ σ₂ lev => let case_RAbsCo := tt in _
| RApp Γ Δ Σ₁ Σ₂ tx te lev => let case_RApp := tt in _
| RLet Γ Δ Σ₁ Σ₂ σ₁ σ₂ lev => let case_RLet := tt in _
| RAbsCo Γ Δ Σ κ σ σ₁ σ₂ lev => let case_RAbsCo := tt in _
| RApp Γ Δ Σ₁ Σ₂ tx te lev => let case_RApp := tt in _
| RLet Γ Δ Σ₁ Σ₂ σ₁ σ₂ lev => let case_RLet := tt in _
- | RCut Γ Δ Σ₁ Σ₁₂ Σ₂ Σ₃ l => let case_RCut := tt in _
- | RLeft Γ Δ Σ₁ Σ₂ Σ l => let case_RLeft := tt in _
- | RRight Γ Δ Σ₁ Σ₂ Σ l => let case_RRight := tt in _
+ | RCut Γ Δ Σ Σ₁ Σ₁₂ Σ₂ Σ₃ l => let case_RCut := tt in _
+ | RLeft Γ Δ Σ₁ Σ₂ Σ l => let case_RLeft := tt in _
+ | RRight Γ Δ Σ₁ Σ₂ Σ l => let case_RRight := tt in _
| RWhere Γ Δ Σ₁ Σ₂ Σ₃ σ₁ σ₂ lev => let case_RWhere := tt in _
| RVoid _ _ l => let case_RVoid := tt in _
| RBrak Γ Δ t ec succ lev => let case_RBrak := tt in _
| RWhere Γ Δ Σ₁ Σ₂ Σ₃ σ₁ σ₂ lev => let case_RWhere := tt in _
| RVoid _ _ l => let case_RVoid := tt in _
| RBrak Γ Δ t ec succ lev => let case_RBrak := tt in _
simpl.
set (drop_lev (ec :: lev) (Σ₁₂ @@@ (ec :: lev))) as x1.
rewrite take_lemma'.
rewrite mapOptionTree_compose.
rewrite mapOptionTree_compose.
rewrite mapOptionTree_compose.
simpl.
set (drop_lev (ec :: lev) (Σ₁₂ @@@ (ec :: lev))) as x1.
rewrite take_lemma'.
rewrite mapOptionTree_compose.
rewrite mapOptionTree_compose.
rewrite mapOptionTree_compose.
set (mapOptionTree flatten_type Σ₁₂) as a.
set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₁)) as b.
set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₂)) as c.
set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₂)) as d.
set (mapOptionTree flatten_type Σ₁₂) as a.
set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₁)) as b.
set (mapOptionTree flatten_leveled_type (drop_lev (ec :: lev) Σ₂)) as c.
set (mapOptionTree (flatten_type ○ unlev) (take_lev (ec :: lev) Σ₂)) as d.
eapply nd_comp; [ idtac | eapply nd_rule; eapply RCut ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
apply nd_prod.
simpl.
eapply nd_comp; [ idtac | eapply nd_rule; eapply RCut ].
eapply nd_comp; [ apply nd_llecnac | idtac ].
apply nd_prod.
simpl.