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Commit b28ab820 authored by Sylvie Boldo's avatar Sylvie Boldo
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Preuve shape_fun_L_cur_eq

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......@@ -682,40 +682,28 @@ rewrite -T_geom_transports_nodes; try easy; f_equal.
unfold node_ref_aux; f_equal; apply ord_inj; easy.
Qed.
Lemma shape_fun_ext : forall (fe1 fe2:FE) (H:fe1 = fe2),
shape_fun fe1 = (castF (eq_sym (f_equal ndof H))
(mapF (castF_fun (eq_sym (f_equal d H))) (shape_fun fe2))).
Proof.
intros fe1 fe2 H; subst.
apply extF; intros i; apply fun_ext; intros x.
rewrite castF_refl.
rewrite mapF_correct; unfold castF_fun; f_equal.
now rewrite castF_refl.
Qed.
Lemma shape_fun_L_cur_eq : forall (vtx_cur :'R^{dL.+1,dL})
(Hvtx : affine_independent vtx_cur),
shape_fun (FE_LagPk_d_cur dL kL dL_pos kL_pos vtx_cur Hvtx) =
shape_fun_cur FE_LagPk_d_ref shape_Lag_ref vtx_cur Hvtx.
Proof.
intros vtx_cur Hvtx; unfold shape_fun_cur.
apply extF; intros i.
generalize (FE_cur_eq vtx_cur Hvtx); intros T.
(*pose (t:= FE_LagPk_d_cur dL kL dL_pos kL_pos vtx_cur Hvtx); fold t in i, T |- *.
assert (V : ndof t = ndof (FE_cur FE_LagPk_d_ref shape_Lag_ref vtx_cur Hvtx)) by easy.
apply trans_eq with
(shape_fun (FE_cur FE_LagPk_d_ref shape_Lag_ref vtx_cur Hvtx)
(cast_ord V i)).
subst t.
generalize (eq_sym T); intros T'.*)
(*apply is_local_shape_fun_inj.
apply shape_fun_correct.
generalize (shape_fun_correct (FE_cur FE_LagPk_d_ref shape_Lag_ref vtx_cur Hvtx)).
intros T.
rewrite -FE_cur_eq in T.
unfold is_local_shape_fun in *.
rewrite -FE_cur_eq.
apply shape_fun_correct.
unfold FE_LagPk_d_ref.*)
(*rewrite -> (FE_cur_eq vtx_cur Hvtx).
apply shape_fun_correct.*)
(*16/10/23: Ce n'est pas urgent *)
Admitted.
intros vtx_cur Hvtx; unfold shape_fun_cur; eapply trans_eq.
apply shape_fun_ext with (H:=FE_cur_eq vtx_cur Hvtx).
rewrite castF_id.
apply extF; intros i; rewrite mapF_correct; apply fun_ext; intros x.
unfold castF_fun; f_equal; now rewrite castF_id.
Qed.
(* From Aide-memoire EF Alexandre Ern : Eq 3.37 p. 63 *)
(* "Ip (v o T) = (Ip v) o T" *)
......
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