(* Basic_2A1: uses: lsx_lleq_trans *)
lemma rsx_reqx_trans (h) (G):
- â\88\80L1,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L1â¦\84 →
- â\88\80L2. L1 â\89\9b[T] L2 â\86\92 G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L2â¦\84.
+ â\88\80L1,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL1â\9d« →
+ â\88\80L2. L1 â\89\9b[T] L2 â\86\92 G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL2â\9d«.
#h #G #L1 #T #H @(rsx_ind … H) -L1
#L1 #_ #IHL1 #L2 #HL12 @rsx_intro
#L #HL2 #HnL2 elim (reqx_lpx_trans … HL2 … HL12) -HL2
(* Basic_2A1: uses: lsx_lpx_trans *)
lemma rsx_lpx_trans (h) (G):
- â\88\80L1,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L1â¦\84 →
- â\88\80L2. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h] L2 â\86\92 G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L2â¦\84.
+ â\88\80L1,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL1â\9d« →
+ â\88\80L2. â\9dªG,L1â\9d« â\8a¢ â¬\88[h] L2 â\86\92 G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL2â\9d«.
#h #G #L1 #T #H @(rsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
elim (reqx_dec L1 L2 T) /3 width=4 by rsx_reqx_trans/
qed-.