[ #L1 #L2 #_ <plus_n_Sm #H destruct
| #K2 #I2 #V2 #L1 #L2 #H1 #H2
elim (destruct_lpair_lpair … H1) -H1 #H1 #H3 #H4 destruct (**) (* destruct lemma needed *)
- elim (IH … H1 ?) -IH -H1 // -H2 /2 width=1/
+ elim (IH … H1) -IH -H1 // -H2 /2 width=1/
]
]
qed-.
elim (plus_xySz_x_false … (sym_eq … H))
| #K2 #I2 #V2 #L1 #L2 #H1 #H2
elim (destruct_lpair_lpair … H1) -H1 #H1 #H3 #H4 destruct (**) (* destruct lemma needed *)
- elim (IH … H1 ?) -IH -H1 // -H2 /2 width=1/
+ elim (IH … H1) -IH -H1 // -H2 /2 width=1/
]
]
qed-.
lemma append_inv_refl_dx: ∀L,K. L @@ K = L → K = ⋆.
#L #K #H
-elim (append_inj_dx … (⋆) … H ?) //
+elim (append_inj_dx … (⋆) … H) //
qed-.
lemma append_inv_pair_dx: ∀I,L,K,V. L @@ K = L.ⓑ{I}V → K = ⋆.ⓑ{I}V.
#I #L #K #V #H
-elim (append_inj_dx … (⋆.ⓑ{I}V) … H ?) //
+elim (append_inj_dx … (⋆.ⓑ{I}V) … H) //
qed-.
lemma length_inv_pos_dx_append: ∀d,L. |L| = d + 1 →
@(ex2_3_intro … (⋆)) // (**) (* explicit constructor *)
| #d #IHd #L #H elim (length_inv_pos_sn … H) -H #I #K #V #H1 #H2 destruct
>H1 in IHd; -H1 #IHd
- elim (IHd K ?) -IHd // #J #L #W #H1 #H2 destruct
+ elim (IHd K) -IHd // #J #L #W #H1 #H2 destruct
@(ex2_3_intro … (L.ⓑ{I}V)) // (**) (* explicit constructor *)
>append_length /2 width=1/
]