include "ground/lib/subset.ma".
include "delayed_updating/syntax/path.ma".
+include "delayed_updating/notation/functions/pitchfork_2.ma".
include "delayed_updating/notation/functions/uptriangle_1.ma".
(* PRETERM ******************************************************************)
(* Note: preterms are subsets of complete paths *)
definition preterm: Type[0] ≝ 𝒫❨path❩.
+definition preterm_grafted: path → preterm → preterm ≝
+ λp,t,q. p;;q ϵ t.
+
+interpretation
+ "grafted (preterm)"
+ 'Pitchfork t p = (preterm_grafted p t).
+
definition preterm_root: preterm → preterm ≝
- λt,p. ∃q. p;;q ϵ t.
+ λt,q. ∃r. q;;r ϵ t.
interpretation
"root (preterm)"