(* Note: the main property of simple terms *)
lemma cpg_inv_appl1_simple (Rs) (Rk) (c) (G) (L):
- â\88\80V1,T1,U. â\9dªG,Lâ\9d« â\8a¢ â\93\90V1.T1 â¬\88[Rs,Rk,c] U â\86\92 ð\9d\90\92â\9dªT1â\9d« →
- â\88\83â\88\83cV,cT,V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â¬\88[Rs,Rk,cV] V2 & â\9dªG,Lâ\9d« ⊢ T1 ⬈[Rs,Rk,cT] T2 & U = ⓐV2.T2 & c = ((↕*cV)∨cT).
+ â\88\80V1,T1,U. â\9d¨G,Lâ\9d© â\8a¢ â\93\90V1.T1 â¬\88[Rs,Rk,c] U â\86\92 ð\9d\90\92â\9d¨T1â\9d© →
+ â\88\83â\88\83cV,cT,V2,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â¬\88[Rs,Rk,cV] V2 & â\9d¨G,Lâ\9d© ⊢ 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