Detection of dead code.

FEM/geom_transf_affine.v

@@ -87,11 +87,12 @@ Qed.
 Lemma T_geom_vtxF : mapF T_geom vtx_ref = vtx.
 Proof. extF; apply T_geom_vtx. Qed.
 
+(* Unused!
 Lemma T_geom_am_lc :
   forall L, sum L = 1 -> T_geom (lin_comb L vtx_ref) = lin_comb L vtx.
 Proof.
 intros; rewrite -!baryc_ms_eq// (am_normal_rev T_geom_am)// T_geom_vtxF; easy.
-Qed.
+Qed.*)
 
 Lemma T_geom_baryc :
   forall L, sum L = 1 ->
@@ -161,11 +162,12 @@ Proof. apply f_inv_can_l. Qed.
 Lemma T_geom_inv_can_r : cancel T_geom_inv (T_geom vtx).
 Proof. apply f_inv_can_r. Qed.
 
+(* Unused!
 Lemma T_geom_inv_bij : bijective T_geom_inv.
 Proof. apply f_inv_bij. Qed.
 
 Lemma T_geom_inv_inj : injective T_geom_inv.
-Proof. apply bij_inj, T_geom_inv_bij. Qed.
+Proof. apply bij_inj, T_geom_inv_bij. Qed.*)
 
 Lemma T_geom_inv_am : aff_map_ms T_geom_inv.
 Proof. apply: am_bij_compat; apply T_geom_am. Qed.
@@ -179,12 +181,13 @@ Proof. rewrite -(T_geom_vtxF vtx) -mapF_comp T_geom_inv_id_l; easy. Qed.
 Lemma T_geom_inv_vtx : forall i, T_geom_inv (vtx i) = vtx_ref i.
 Proof. intro; rewrite -T_geom_inv_vtxF; easy. Qed.
 
+(* Unused!
 Lemma T_geom_inv_am_lc :
   forall L, sum L = 1 -> T_geom_inv (lin_comb L vtx) = lin_comb L vtx_ref.
 Proof.
 intros; rewrite -!baryc_ms_eq//
     (am_normal_rev T_geom_inv_am)// T_geom_inv_vtxF; easy.
-Qed.
+Qed.*)
 
 Lemma T_geom_inv_baryc :
   forall L, sum L = 1 ->
@@ -217,6 +220,7 @@ Proof.
 move=>> [L HL1 HL2]; unfold K_geom, preimage; rewrite T_geom_inv_baryc; easy.
 Qed.
 
+(* Unused!
 Lemma T_geom_bijS_K_geom_spec :
   bijS_spec K_geom_ref K_geom (T_geom vtx) (T_geom_inv Hvtx).
 Proof.
@@ -241,7 +245,7 @@ intros x_ref _; apply T_geom_inv_can_l.
 Qed.
 
 Lemma T_geom_inv_bijS_K_geom : bijS K_geom K_geom_ref (T_geom_inv Hvtx).
-Proof. apply (BijS _ T_geom_inv_bijS_K_geom_spec). Qed.
+Proof. apply (BijS _ T_geom_inv_bijS_K_geom_spec). Qed.*)
 
 (**
  #<A HREF="##RR9557v1">#[[RR9557v1]]#</A>#
@@ -339,17 +343,19 @@ Lemma T_geom_permutF_inv_can_r :
   cancel T_geom_permutF_inv (T_geom_permutF vtx pi_d).
 Proof. apply f_inv_can_r. Qed.
 
+(* Unused!
 Lemma T_geom_permutF_inv_id_l :
   T_geom_permutF_inv \o T_geom_permutF vtx pi_d = id.
 Proof. apply f_inv_id_l. Qed.
 
 Lemma T_geom_permutF_inv_id_r :
   T_geom_permutF vtx pi_d \o T_geom_permutF_inv = id.
-Proof. apply f_inv_id_r. Qed.
+Proof. apply f_inv_id_r. Qed.*)
 
+(* Unused!
 Lemma T_geom_permutF_inv_correct :
   T_geom_permutF_inv = T_geom_inv (aff_indep_permutF pi_d_bij Hvtx).
-Proof. apply f_inv_uniq_l, f_inv_can_l. Qed.
+Proof. apply f_inv_uniq_l, f_inv_can_l. Qed.*)
 
 (**
  #<A HREF="##RR9557v1">#[[RR9557v1]]#</A>#
@@ -381,10 +387,11 @@ intro; unfold T_geom_permutF, T_geom;
     rewrite LagPd1_ref_sum; apply invertible_one.
 Qed.
 
+(* Unused!
 Lemma T_geom_permutF_vtx :
   forall i,
     T_geom_permutF vtx pi_d (vtx_ref i) = T_geom vtx (vtx_ref (pi_d i)).
-Proof. intro; unfold T_geom_permutF; rewrite !T_geom_vtx; easy. Qed.
+Proof. intro; unfold T_geom_permutF; rewrite !T_geom_vtx; easy. Qed.*)
 
 Lemma T_geom_permutF_skipF :
   forall i j,
@@ -405,9 +412,10 @@ Variable vtx : 'R^{d.+1,d}.
 Definition T_geom_transpF (i0 : 'I_d.+1) : 'R^d -> 'R^d :=
   T_geom_permutF vtx (transp_ord ord_max i0).
 
+(* Unused!
 Lemma T_geom_transpF_correct :
   forall i0, T_geom_transpF i0 = T_geom (transpF ord_max i0 vtx).
-Proof. easy. Qed.
+Proof. easy. Qed.*)
 
 End T_geom_transpF_Def.
 
@@ -440,15 +448,18 @@ Variable vtx : 'R^{d.+1,d}.
 Definition T_geom_Hface (i : 'I_d.+1) : 'R^d1 -> 'R^d :=
   T_geom vtx \o inj_Hface_ref i.
 
+(* Unused!
 Lemma T_geom_Hface_0 :
   forall {i}, i = ord0 -> T_geom_Hface i = T_geom vtx \o part1F0.
-Proof. intros; unfold T_geom_Hface; rewrite inj_Hface_ref_0; easy. Qed.
+Proof. intros; unfold T_geom_Hface; rewrite inj_Hface_ref_0; easy. Qed.*)
 
+(* Unused!
 Lemma T_geom_Hface_S :
   forall {i} (Hi : i <> ord0),
     T_geom_Hface i = T_geom vtx \o (insert0F^~ (lower_S Hi)).
-Proof. move=>>; unfold T_geom_Hface; rewrite inj_Hface_ref_S; easy. Qed.
+Proof. move=>>; unfold T_geom_Hface; rewrite inj_Hface_ref_S; easy. Qed.*)
 
+(* Unused!
 Lemma T_geom_Hface_0_correct :
   forall {i} (Hi : i = ord0) x_ref,
     T_geom_Hface i x_ref = barycenter_ms (LagPd1_ref^~ x_ref) (skipF vtx i).
@@ -462,8 +473,9 @@ destruct (ord_eq_dec j ord0) as [-> | Hj].
 rewrite LagPd1_ref_0// insertF_correct_l; easy.
 move: (proj1 (ord_n0_gt_equiv d) Hj) => Hj'.
 rewrite LagPd1_ref_S insertF_correct_rr; f_equal; apply lower_S_ext.
-Qed.
+Qed.*)
 
+(* Unused!
 Lemma T_geom_Hface_S_correct :
   forall {i} (Hi : i <> ord0) x_ref,
     T_geom_Hface i x_ref = barycenter_ms (LagPd1_ref^~ x_ref) (skipF vtx i).
@@ -486,9 +498,9 @@ rewrite (skip_ord_correct_l _ _ H'); apply ord_inj; simpl. admit.
 (* *)
 assert (H' : ~ (lower_S Hj < lower_S Hi)%coq_nat) by admit.
 rewrite (skip_ord_correct_r _ _ H'); apply ord_inj; simpl. admit.
-Admitted.
+Admitted.*)
 
-(* Hopefully, this should be useless! *)
+(* Hopefully, this should be useless!
 Lemma T_geom_Hface_0_lc :
   forall x_ref,
     T_geom_Hface ord0 x_ref = scal (1 - sum x_ref) (vtx ord1) +
@@ -496,9 +508,9 @@ Lemma T_geom_Hface_0_lc :
 Proof.
 intro; rewrite T_geom_Hface_0_correct// baryc_ms_eq; [| apply LagPd1_ref_sum].
 rewrite lc_ind_l LagPd1_ref_0// skipF_first liftF_S_0 LagPd1_ref_SF; easy.
-Qed.
+Qed.*)
 
-(* Hopefully, this should be useless! *)
+(* Hopefully, this should be useless!
 Lemma T_geom_Hface_S_lc :
   forall i x_ref, i <> ord0 ->
     T_geom_Hface i x_ref = scal (1 - sum x_ref) (vtx ord0) +
@@ -508,9 +520,9 @@ intros; rewrite T_geom_Hface_S_correct// baryc_ms_eq; [| apply LagPd1_ref_sum].
 assert (Hi' : (@ord0 d1 < i)%coq_nat) by now apply ord_n0_gt_equiv.
 rewrite lc_ind_l LagPd1_ref_0// skipF_correct_l//
     widenF_S_0 LagPd1_ref_SF; easy.
-Qed.
+Qed.*)
 
-(* Hopefully, this should be useless! *)
+(* Hopefully, this should be useless!
 (**
  #<A HREF="##RR9557v1">#[[RR9557v1]]#</A>#
  Lem 1584, Eq (9.72), pp. 94-95.#<BR>#
@@ -524,9 +536,9 @@ Proof.
 intros; rewrite T_geom_Hface_0_lc.
 rewrite scal_minus_l scal_one -plus_assoc -minus_sym.
 rewrite lc_minus_r lc_constF_r; easy.
-Qed.
+Qed.*)
 
-(* Hopefully, this should be useless! *)
+(* Hopefully, this should be useless!
 (**
  #<A HREF="##RR9557v1">#[[RR9557v1]]#</A>#
  Lem 1584, Eq (9.73), pp. 94-95.#<BR>#
@@ -540,7 +552,7 @@ Proof.
 intros; rewrite T_geom_Hface_S_lc//.
 rewrite scal_minus_l scal_one -plus_assoc -minus_sym.
 rewrite lc_minus_r lc_constF_r; easy.
-Qed.
+Qed.*)
 
 (**
  #<A HREF="##RR9557v1">#[[RR9557v1]]#</A>#
@@ -550,7 +562,7 @@ Proof.
 intro; apply am_comp_ms; [apply inj_Hface_ref_am | apply T_geom_am].
 Qed.
 
-(* Hopefully, this should be useless! *)
+(* Hopefully, this should be useless!
 (**
  #<A HREF="##RR9557v1">#[[RR9557v1]]#</A>#
  Lem 1584, Eq (9.73), pp. 94-95.#<BR>#
@@ -564,9 +576,9 @@ Proof.
 intros x_ref; unfold fct_lm_ms; rewrite fct_lm_ms_eq.
 rewrite plus_zero_l !T_geom_Hface_0_lc_alt lc_zero_l plus_zero_r.
 apply: minus_plus_l.
-Qed.
+Qed.*)
 
-(* Hopefully, this should be useless! *)
+(* Hopefully, this should be useless!
 (**
  #<A HREF="##RR9557v1">#[[RR9557v1]]#</A>#
  Lem 1584, Eq (9.73), pp. 94-95.#<BR>#
@@ -580,7 +592,7 @@ Proof.
 intros i x_ref Hi; unfold fct_lm_ms; rewrite fct_lm_ms_eq.
 rewrite plus_zero_l !T_geom_Hface_S_lc_alt// lc_zero_l plus_zero_r.
 apply: minus_plus_l.
-Qed.
+Qed.*)
 
 (**
  #<A HREF="##RR9557v1">#[[RR9557v1]]#</A>#