(* T-UNBOUND WHD EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS **************)
definition cpmuwe (h) (n) (G) (L): relation2 term term ≝
(* T-UNBOUND WHD EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS **************)
definition cpmuwe (h) (n) (G) (L): relation2 term term ≝
- λT1,T2. â\88§â\88§ â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n,h] T2 & â¦\83G,Lâ¦\84 ⊢ ➡𝐍𝐖*[h] T2.
+ λT1,T2. â\88§â\88§ â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[n,h] T2 & â\9dªG,Lâ\9d« ⊢ ➡𝐍𝐖*[h] T2.
interpretation "t-unbound whd evaluation for t-bound context-sensitive parallel rt-transition (term)"
'PRedEvalWStar h n G L T1 T2 = (cpmuwe h n G L T1 T2).
definition R_cpmuwe (h) (G) (L) (T): predicate nat ≝
interpretation "t-unbound whd evaluation for t-bound context-sensitive parallel rt-transition (term)"
'PRedEvalWStar h n G L T1 T2 = (cpmuwe h n G L T1 T2).
definition R_cpmuwe (h) (G) (L) (T): predicate nat ≝
(* Basic properties *********************************************************)
lemma cpmuwe_intro (h) (n) (G) (L):
(* Basic properties *********************************************************)
lemma cpmuwe_intro (h) (n) (G) (L):
- â\88\80T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[n,h] T2 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â\9e¡ð\9d\90\8dð\9d\90\96*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ➡*𝐍𝐖*[h,n] T2.
+ â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[n,h] T2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\9e¡ð\9d\90\8dð\9d\90\96*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*𝐍𝐖*[h,n] T2.
/2 width=1 by conj/ qed.
(* Advanced properties ******************************************************)
lemma cpmuwe_sort (h) (n) (G) (L) (T):
/2 width=1 by conj/ qed.
(* Advanced properties ******************************************************)
lemma cpmuwe_sort (h) (n) (G) (L) (T):
- â\88\80s. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[n,h] â\8b\86s â\86\92 â¦\83G,Lâ¦\84 ⊢ T ➡*𝐍𝐖*[h,n] ⋆s.
+ â\88\80s. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[n,h] â\8b\86s â\86\92 â\9dªG,Lâ\9d« ⊢ T ➡*𝐍𝐖*[h,n] ⋆s.
/3 width=5 by cnuw_sort, cpmuwe_intro/ qed.
lemma cpmuwe_ctop (h) (n) (G) (T):
/3 width=5 by cnuw_sort, cpmuwe_intro/ qed.
lemma cpmuwe_ctop (h) (n) (G) (T):
- â\88\80i. â¦\83G,â\8b\86â¦\84 â\8a¢ T â\9e¡*[n,h] #i â\86\92 â¦\83G,â\8b\86â¦\84 ⊢ T ➡*𝐍𝐖*[h,n] #i.
+ â\88\80i. â\9dªG,â\8b\86â\9d« â\8a¢ T â\9e¡*[n,h] #i â\86\92 â\9dªG,â\8b\86â\9d« ⊢ T ➡*𝐍𝐖*[h,n] #i.
/3 width=5 by cnuw_ctop, cpmuwe_intro/ qed.
lemma cpmuwe_zero_unit (h) (n) (G) (L) (T):
/3 width=5 by cnuw_ctop, cpmuwe_intro/ qed.
lemma cpmuwe_zero_unit (h) (n) (G) (L) (T):
- â\88\80I. â¦\83G,L.â\93¤{I}â¦\84 â\8a¢ T â\9e¡*[n,h] #0 â\86\92 â¦\83G,L.â\93¤{I}â¦\84 ⊢ T ➡*𝐍𝐖*[h,n] #0.
+ â\88\80I. â\9dªG,L.â\93¤[I]â\9d« â\8a¢ T â\9e¡*[n,h] #0 â\86\92 â\9dªG,L.â\93¤[I]â\9d« ⊢ T ➡*𝐍𝐖*[h,n] #0.
/3 width=6 by cnuw_zero_unit, cpmuwe_intro/ qed.
lemma cpmuwe_gref (h) (n) (G) (L) (T):
/3 width=6 by cnuw_zero_unit, cpmuwe_intro/ qed.
lemma cpmuwe_gref (h) (n) (G) (L) (T):
- â\88\80l. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[n,h] §l â\86\92 â¦\83G,Lâ¦\84 ⊢ T ➡*𝐍𝐖*[h,n] §l.
+ â\88\80l. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[n,h] §l â\86\92 â\9dªG,Lâ\9d« ⊢ T ➡*𝐍𝐖*[h,n] §l.
/3 width=5 by cnuw_gref, cpmuwe_intro/ qed.
(* Basic forward lemmas *****************************************************)
lemma cpmuwe_fwd_cpms (h) (n) (G) (L):
/3 width=5 by cnuw_gref, cpmuwe_intro/ qed.
(* Basic forward lemmas *****************************************************)
lemma cpmuwe_fwd_cpms (h) (n) (G) (L):
- â\88\80T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*ð\9d\90\8dð\9d\90\96*[h,n] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ➡*[n,h] T2.
+ â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*ð\9d\90\8dð\9d\90\96*[h,n] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[n,h] T2.