updating the structures for sorts

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / syntax / sh_lt.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/sh_lt.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/sh_lt.ma
index 459d4d16bce3ae285c1cff8564bda5a4a9ca1fad..494436476eb1fc18192ba917277de91e72f62827 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/sh_lt.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/sh_lt.ma
@@ -12,25 +12,30 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "static_2/syntax/sort.ma".
+include "static_2/syntax/sh_props.ma".
 
 (* SORT HIERARCHY ***********************************************************)
 
-record is_lt (h): Prop ≝
+(* strict monotonicity condition *)
+record sh_lt (h): Prop ≝
 {
-  next_lt: ∀s. s < ⫯[h]s (* strict monotonicity condition *)
+  next_lt: ∀s. s < ⫯[h]s
 }.
 
 (* Basic properties *********************************************************)
 
-lemma nexts_le (h): is_lt h → ∀s,n. s ≤ (next h)^n s.
+lemma nexts_le (h): sh_lt h → ∀s,n. s ≤ (next h)^n s.
 #h #Hh #s #n elim n -n [ // ] normalize #n #IH
 lapply (next_lt … Hh ((next h)^n s)) #H
 lapply (le_to_lt_to_lt … IH H) -IH -H /2 width=2 by lt_to_le/
 qed.
 
-lemma nexts_lt (h): is_lt h → ∀s,n. s < (next h)^(↑n) s.
+lemma nexts_lt (h): sh_lt h → ∀s,n. s < (next h)^(↑n) s.
 #h #Hh #s #n normalize
 lapply (nexts_le … Hh s n) #H
 @(le_to_lt_to_lt … H) /2 width=1 by next_lt/
 qed.
+
+axiom sh_lt_dec (h): sh_lt h → sh_decidable h.
+
+axiom sh_lt_acyclic (h): sh_lt h → sh_acyclic h.