(* *)
(**************************************************************************)
-include "basic_2/grammar/term_simple.ma".
+include "static_2/syntax/term_simple.ma".
include "basic_2/rt_transition/cpg.ma".
-(* CONTEXT-SENSITIVE GENERIC PARALLEL RT-TRANSITION FOR TERMS ***************)
+(* BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *****************)
(* Properties with simple terms *********************************************)
(* Note: the main property of simple terms *)
-lemma cpg_inv_appl1_simple: ∀c,h,G,L,V1,T1,U. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡[c, h] U → 𝐒⦃T1⦄ →
- ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ➡[cV, h] V2 & ⦃G, L⦄ ⊢ T1 ➡[cT, h] T2 &
- U = ⓐV2.T2 & c = (↓cV)+cT.
-#c #h #G #L #V1 #T1 #U #H #HT1 elim (cpg_inv_appl1 … H) -H *
+lemma cpg_inv_appl1_simple (Rs) (Rk) (c) (G) (L):
+ ∀V1,T1,U. ❪G,L❫ ⊢ ⓐV1.T1 ⬈[Rs,Rk,c] U → 𝐒❪T1❫ →
+ ∃∃cV,cT,V2,T2. ❪G,L❫ ⊢ V1 ⬈[Rs,Rk,cV] V2 & ❪G,L❫ ⊢ T1 ⬈[Rs,Rk,cT] T2 & U = ⓐV2.T2 & c = ((↕*cV)∨cT).
+#Rs #Rk #c #G #L #V1 #T1 #U #H #HT1 elim (cpg_inv_appl1 … H) -H *
[ /2 width=8 by ex4_4_intro/
| #cV #cW #cT #p #V2 #W1 #W2 #U1 #U2 #_ #_ #_ #H destruct
elim (simple_inv_bind … HT1)