3 Require Export pr0_defs.
5 Inductive pr1 : T -> T -> Prop :=
6 | pr1_r : (t:?) (pr1 t t)
7 | pr1_u : (t2,t1:?) (pr0 t1 t2) -> (t3:?) (pr1 t2 t3) -> (pr1 t1 t3).
9 Hint pr1 : ltlc := Constructors pr1.
11 Section pr1_props. (******************************************************)
13 Theorem pr1_pr0 : (t1,t2:?) (pr0 t1 t2) -> (pr1 t1 t2).
17 Theorem pr1_t : (t2,t1:?) (pr1 t1 t2) ->
18 (t3:?) (pr1 t2 t3) -> (pr1 t1 t3).
19 Intros t2 t1 H; XElim H; XEAuto.
24 Hints Resolve pr1_pr0 pr1_t : ltlc.