(* transitions *)
inductive rtm_step: relation rtm ≝
-| rtm_ldrop : ∀G,u,E,I,t,F,V,S,i.
- rtm_step (mk_rtm G u (E. ④{I} {t, F, V}) S (#(i + 1)))
+| rtm_ldrop : ∀G,u,E,I,t,D,V,S,i.
+ rtm_step (mk_rtm G u (E. ④{I} {t, D, V}) S (#(i + 1)))
(mk_rtm G u E S (#i))
-| rtm_ldelta: ∀G,u,E,t,F,V,S.
- rtm_step (mk_rtm G u (E. ④{Abbr} {t, F, V}) S (#0))
- (mk_rtm G u F S V)
-| rtm_ltype : ∀G,u,E,t,F,V,S.
- rtm_step (mk_rtm G u (E. ④{Abst} {t, F, V}) S (#0))
- (mk_rtm G u F S V)
+| rtm_ldelta: ∀G,u,E,t,D,V,S.
+ rtm_step (mk_rtm G u (E. ④{Abbr} {t, D, V}) S (#0))
+ (mk_rtm G u D S V)
+| rtm_ltype : ∀G,u,E,t,D,V,S.
+ rtm_step (mk_rtm G u (E. ④{Abst} {t, D, V}) S (#0))
+ (mk_rtm G u D S V)
| rtm_gdrop : ∀G,I,V,u,E,S,p. p < |G| →
rtm_step (mk_rtm (G. ⓑ{I} V) u E S (§p))
(mk_rtm G u E S (§p))
| rtm_appl : ∀G,u,E,S,V,T.
rtm_step (mk_rtm G u E S (ⓐV. T))
(mk_rtm G u E ({E, V} @ S) T)
-| rtm_beta : ∀G,u,E,F,V,S,W,T.
- rtm_step (mk_rtm G u E ({F, V} @ S) (+ⓛW. T))
- (mk_rtm G u (E. ④{Abbr} {u, F, V}) S T)
+| rtm_beta : ∀G,u,E,D,V,S,W,T.
+ rtm_step (mk_rtm G u E ({D, V} @ S) (+ⓛW. T))
+ (mk_rtm G u (E. ④{Abbr} {u, D, V}) S T)
| rtm_push : ∀G,u,E,W,T.
- rtm_step (mk_rtm G u E ⟠ (+ⓛW. T))
- (mk_rtm G (u + 1) (E. ④{Abst} {u, E, W}) ⟠ T)
+ rtm_step (mk_rtm G u E (⟠) (+ⓛW. T))
+ (mk_rtm G (u + 1) (E. ④{Abst} {u, E, W}) (⟠) T)
| rtm_theta : ∀G,u,E,S,V,T.
rtm_step (mk_rtm G u E S (+ⓓV. T))
(mk_rtm G u (E. ④{Abbr} {u, E, V}) S T)