some more changes and corrections

[helm.git] / helm / coq-contribs / LAMBDA-TYPES / pc1_props.v

diff --git a/helm/coq-contribs/LAMBDA-TYPES/pc1_props.v b/helm/coq-contribs/LAMBDA-TYPES/pc1_props.v
new file mode 100644 (file)
index 0000000..840a79c
--- /dev/null
+++ b/helm/coq-contribs/LAMBDA-TYPES/pc1_props.v
@@ -0,0 +1,25 @@
+Require pr1_confluence.
+Require pc1_defs. 
+
+(*#* #stop file *)
+
+   Section pc1_trans. (******************************************************)
+
+      Theorem pc1_t: (t2,t1:?) (pc1 t1 t2) ->
+                     (t3:?) (pc1 t2 t3) -> (pc1 t1 t3).
+      Intros; Repeat Pc1Unfold; Pr1Confluence; XEAuto.
+      Qed.
+
+      Theorem pc1_pr0_u2: (t0,t1:?) (pr0 t0 t1) ->
+                          (t2:?) (pc1 t0 t2) -> (pc1 t1 t2).
+      Intros; Apply (pc1_t t0); XAuto.
+      Qed.
+
+      Theorem pc1_tail: (u1,u2:?) (pc1 u1 u2) -> (t1,t2:?) (pc1 t1 t2) ->
+                        (k:?) (pc1 (TTail k u1 t1) (TTail k u2 t2)).
+      Intros; EApply pc1_t; [ EApply pc1_tail_1 | EApply pc1_tail_2 ]; XAuto.
+      Qed.
+
+   End pc1_trans.
+
+      Hints Resolve pc1_t pc1_tail : ltlc.