partial commit in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / lsubf_lsubf.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubf.ma b/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubf.ma
index 79f33abdad8f77bf507ef12a273621fc3494d3c9..8ad9f517d929336cd921b0fe86e8f7fe0801563c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubf.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubf.ma
@@ -19,23 +19,24 @@ include "static_2/static/lsubf.ma".
 
 (* Main properties **********************************************************)
 
-theorem lsubf_sor: ∀K,L,g1,f1. ⦃K, g1⦄ ⫃𝐅* ⦃L, f1⦄ →
-                   ∀g2,f2. ⦃K, g2⦄ ⫃𝐅* ⦃L, f2⦄ →
-                   ∀g. g1 ⋓ g2 ≘ g → ∀f. f1 ⋓ f2 ≘ f → ⦃K, g⦄ ⫃𝐅* ⦃L, f⦄.
+theorem lsubf_sor:
+        ∀K,L,g1,f1. ❪K,g1❫ ⫃𝐅+ ❪L,f1❫ →
+        ∀g2,f2. ❪K,g2❫ ⫃𝐅+ ❪L,f2❫ →
+        ∀g. g1 ⋓ g2 ≘ g → ∀f. f1 ⋓ f2 ≘ f → ❪K,g❫ ⫃𝐅+ ❪L,f❫.
 #K elim K -K
 [ #L #g1 #f1 #H1 #g2 #f2 #H2 #g #Hg #f #Hf
   elim (lsubf_inv_atom1 … H1) -H1 #H1 #H destruct
   lapply (lsubf_inv_atom … H2) -H2 #H2
-  /5 width=4 by lsubf_atom, sor_mono, sor_eq_repl_back2, sor_eq_repl_back1/
+  /5 width=4 by lsubf_atom, pr_sor_mono, pr_sor_eq_repl_back_dx, pr_sor_eq_repl_back_sn/
 | #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 … Hg) -Hg [|*: // ] #y #Hy #H destruct
+  elim (pr_map_split_tl g1) * #y1 #H destruct
+  elim (pr_map_split_tl g2) * #y2 #H destruct
+  [ elim (pr_sor_inv_push_bi … Hg) -Hg [|*: // ] #y #Hy #H destruct
     elim (lsubf_inv_push1 … H1) -H1 #x1 #Z1 #Y1 #H1 #H #H0 destruct
     elim (lsubf_inv_push_sn … H2) -H2 #x2 #H2 #H destruct
-    elim (sor_inv_ppx … Hf) -Hf [|*: // ] #x #Hx #H destruct
+    elim (pr_sor_inv_push_bi … Hf) -Hf [|*: // ] #x #Hx #H destruct
     /3 width=8 by lsubf_push/
-  | elim (sor_inv_pnx … Hg) -Hg [|*: // ] #y #Hy #H destruct
+  | elim (pr_sor_inv_push_next … Hg) -Hg [|*: // ] #y #Hy #H destruct
     elim (lsubf_inv_push1 … H1) -H1 #x1 #Z1 #Y1 #H1 #H #H0 destruct
     generalize in match H2; -H2 cases J -J #J [| #V ] #H2
     [ elim (lsubf_inv_unit1 … H2) -H2 #x2 #Y2 #H2 #H #H0 destruct
@@ -45,9 +46,9 @@ theorem lsubf_sor: ∀K,L,g1,f1. ⦃K, g1⦄ ⫃𝐅* ⦃L, f1⦄ →
       | #y3 #y4 #x2 #Z2 #Y2 #H2 #Hy3 #Hy2 #H #H0 destruct
       ]
     ]
-    elim (sor_inv_pnx … 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 … Hg) -Hg [|*: // ] #y #Hy #H destruct
+    elim (pr_sor_inv_push_next … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
+    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, pr_sor_assoc_sn/
+  | elim (pr_sor_inv_next_push … Hg) -Hg [|*: // ] #y #Hy #H destruct
     elim (lsubf_inv_push1 … H2) -H2 #x2 #Z2 #Y2 #H2 #H #H0 destruct
     generalize in match H1; -H1 cases J -J #J [| #V ] #H1
     [ elim (lsubf_inv_unit1 … H1) -H1 #x1 #Y1 #H1 #H #H0 destruct
@@ -57,9 +58,9 @@ theorem lsubf_sor: ∀K,L,g1,f1. ⦃K, g1⦄ ⫃𝐅* ⦃L, f1⦄ →
       | #y3 #y4 #x1 #Z1 #Y1 #H1 #Hy3 #Hy1 #H #H0 destruct
       ]
     ]
-    elim (sor_inv_npx … 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 … Hg) -Hg [|*: // ] #y #Hy #H destruct
+    elim (pr_sor_inv_next_push … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
+    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, pr_sor_comm_23/
+  | elim (pr_sor_inv_next_bi … 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 … H1) -H1 #x1 #Y1 #H1 #H #H0 destruct
       elim (lsubf_inv_bind_sn … H2) -H2 #x2 #H2 #H destruct
@@ -69,15 +70,15 @@ theorem lsubf_sor: ∀K,L,g1,f1. ⦃K, g1⦄ ⫃𝐅* ⦃L, f1⦄ →
       | #y3 #y4 #x1 #Y1 #W #U #H1 #Hy3 #Hy1 #H #H0 #H3 #H4 destruct
         elim (lsubf_inv_beta_sn … H2) -H2 #z3 #z4 #x2 #H2 #Hz3 #Hy2 #H destruct
         lapply (frees_mono … Hz3 … Hy3) -Hz3 #H3
-        lapply (sor_eq_repl_back2 … Hy2 … H3) -z3 #Hy2
+        lapply (pr_sor_eq_repl_back_dx … Hy2 … H3) -z3 #Hy2
       | #y3 #y4 #x1 #Z1 #Y1 #H1 #Hy3 #Hy1 #H #H0 destruct
         elim (lsubf_inv_unit_sn … H2) -H2 #z3 #z4 #x2 #H2 #Hz3 #Hy2 #H destruct
         lapply (frees_mono … Hz3 … Hy3) -Hz3 #H3
-        lapply (sor_eq_repl_back2 … Hy2 … H3) -z3 #Hy2
+        lapply (pr_sor_eq_repl_back_dx … Hy2 … H3) -z3 #Hy2
       ]
     ]
-    elim (sor_inv_nnx … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
-    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, sor_coll_dx/
+    elim (pr_sor_inv_next_bi … Hf) -Hf [1,6,11,16:|*: // ] #x #Hx #H destruct
+    /3 width=12 by lsubf_unit, lsubf_beta, lsubf_bind, pr_sor_coll_dx/
   ]
 ]
 qed-.