+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/static/frees_frees.ma".
-include "basic_2/static/lsubf.ma".
-
-(* RESTRICTED REFINEMENT FOR CONTEXT-SENSITIVE FREE VARIABLES ***************)
-
-(* Main properties **********************************************************)
-
-theorem lsubf_sor: āK,L,g1,f1. ā¦K, g1ā¦ ā«š
* ā¦L, f1ā¦ ā
- āg2,f2. ā¦K, g2ā¦ ā«š
* ā¦L, f2ā¦ ā
- āg. g1 ā g2 ā g ā āf. f1 ā f2 ā f ā ā¦K, gā¦ ā«š
* ā¦L, fā¦.
-#K elim K -K
-[ #L #g1 #f1 #H1 #g2 #f2 #H2 #g #Hg #f #Hf
- elim (lsubf_inv_atom1 ā¦ H1) -H1 #H1 #H destruct
- lapply (lsubf_inv_atom ā¦ H2) -H2 #H2
- /5 width=4 by lsubf_atom, sor_mono, sor_eq_repl_back2, sor_eq_repl_back1/
-| #K #J #IH #L #g1 #f1 #H1 #g2 #f2 #H2 #g #Hg #f #Hf
- elim (pn_split g1) * #y1 #H destruct
- elim (pn_split g2) * #y2 #H destruct
- [ elim (sor_inv_ppx ā¦ Hg) -Hg [|*: // ] #y #Hy #H destruct
- elim (lsubf_inv_push1 ā¦ H1) -H1 #x1 #Z1 #Y1 #H1 #H #H0 destruct
- elim (lsubf_inv_push_sn ā¦ H2) -H2 #x2 #H2 #H destruct
- elim (sor_inv_ppx ā¦ Hf) -Hf [|*: // ] #x #Hx #H destruct
- /3 width=8 by lsubf_push/
- | elim (sor_inv_pnx ā¦ Hg) -Hg [|*: // ] #y #Hy #H destruct
- elim (lsubf_inv_push1 ā¦ H1) -H1 #x1 #Z1 #Y1 #H1 #H #H0 destruct
- generalize in match H2; -H2 cases J -J #J [| #V ] #H2
- [ elim (lsubf_inv_unit1 ā¦ H2) -H2 #x2 #Y2 #H2 #H #H0 destruct
- | elim (lsubf_inv_pair1 ā¦ H2) -H2 *
- [ #x2 #Z2 #H2 #H #H0 destruct
- | #y3 #y4 #x2 #Y2 #W #U #H2 #Hy3 #Hy2 #H #H0 #H3 #H4 destruct
- | #y3 #y4 #x2 #Z2 #Y2 #H2 #Hy3 #Hy2 #H #H0 destruct
- ]
- ]
- elim (sor_inv_pnx ā¦ Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
- /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, sor_assoc_sn/
- | elim (sor_inv_npx ā¦ Hg) -Hg [|*: // ] #y #Hy #H destruct
- elim (lsubf_inv_push1 ā¦ H2) -H2 #x2 #Z2 #Y2 #H2 #H #H0 destruct
- generalize in match H1; -H1 cases J -J #J [| #V ] #H1
- [ elim (lsubf_inv_unit1 ā¦ H1) -H1 #x1 #Y1 #H1 #H #H0 destruct
- | elim (lsubf_inv_pair1 ā¦ H1) -H1 *
- [ #x1 #Z1 #H1 #H #H0 destruct
- | #y3 #y4 #x1 #Y1 #W #U #H1 #Hy3 #Hy1 #H #H0 #H3 #H4 destruct
- | #y3 #y4 #x1 #Z1 #Y1 #H1 #Hy3 #Hy1 #H #H0 destruct
- ]
- ]
- elim (sor_inv_npx ā¦ Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
- /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, sor_comm_23/
- | elim (sor_inv_nnx ā¦ Hg) -Hg [|*: // ] #y #Hy #H destruct
- generalize in match H2; generalize in match H1; -H1 -H2 cases J -J #J [| #V ] #H1 #H2
- [ elim (lsubf_inv_unit1 ā¦ H1) -H1 #x1 #Y1 #H1 #H #H0 destruct
- elim (lsubf_inv_bind_sn ā¦ H2) -H2 #x2 #H2 #H destruct
- | elim (lsubf_inv_pair1 ā¦ H1) -H1 *
- [ #x1 #Z1 #H1 #H #H0 destruct
- elim (lsubf_inv_bind_sn ā¦ H2) -H2 #x2 #H2 #H destruct
- | #y3 #y4 #x1 #Y1 #W #U #H1 #Hy3 #Hy1 #H #H0 #H3 #H4 destruct
- elim (lsubf_inv_beta_sn ā¦ H2) -H2 #z3 #z4 #x2 #H2 #Hz3 #Hy2 #H destruct
- lapply (frees_mono ā¦ Hz3 ā¦ Hy3) -Hz3 #H3
- lapply (sor_eq_repl_back2 ā¦ Hy2 ā¦ H3) -z3 #Hy2
- | #y3 #y4 #x1 #Z1 #Y1 #H1 #Hy3 #Hy1 #H #H0 destruct
- elim (lsubf_inv_unit_sn ā¦ H2) -H2 #z3 #z4 #x2 #H2 #Hz3 #Hy2 #H destruct
- lapply (frees_mono ā¦ Hz3 ā¦ Hy3) -Hz3 #H3
- lapply (sor_eq_repl_back2 ā¦ Hy2 ā¦ H3) -z3 #Hy2
- ]
- ]
- elim (sor_inv_nnx ā¦ Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
- /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, sor_coll_dx/
- ]
-]
-qed-.