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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 set "baseuri" "cic:/matita/PREDICATIVE-TOPOLOGY/class_le".
17 include "class_defs.ma".
19 theorem cle_cl: \forall C,c1,c2. cle ? c1 c2 \to cin C c1 \land cin C c2.
20 intros; elim H; clear H; clear c2;
21 [| decompose H2 ]; auto.
24 theorem cle_trans: \forall C,c1,c2. cle C c1 c2 \to
25 \forall c3. cle ? c3 c1 \to cle ? c3 c2.
26 intros 4; elim H; clear H; clear c2;
27 [| apply ceq_sing; [||| apply H4 ]]; auto.