- some renaming according to the written version of basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / sh.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/sh.ma b/matita/matita/contribs/lambdadelta/basic_2/static/sh.ma
index 0d09320cc871665e968a39e15b0f3434c31d917a..824e37e1fd942bd1a0d5fac70af321005a9234a3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/sh.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/sh.ma
@@ -27,18 +27,18 @@ definition sh_N: sh ≝ mk_sh S ….
 
 (* Basic properties *********************************************************)
 
-lemma nexts_le: ∀h,k,l. k ≤ (next h)^l k.
-#h #k #l elim l -l // normalize #l #IHl
-lapply (next_lt h ((next h)^l k)) #H
-lapply (le_to_lt_to_lt … IHl H) -IHl -H /2 width=2 by lt_to_le/
+lemma nexts_le: ∀h,k,d. k ≤ (next h)^d k.
+#h #k #d elim d -d // normalize #d #IHd
+lapply (next_lt h ((next h)^d k)) #H
+lapply (le_to_lt_to_lt … IHd H) -IHd -H /2 width=2 by lt_to_le/
 qed.
 
-lemma nexts_lt: ∀h,k,l. k < (next h)^(l+1) k.
-#h #k #l >iter_SO
-lapply (nexts_le h k l) #H
+lemma nexts_lt: ∀h,k,d. k < (next h)^(d+1) k.
+#h #k #d >iter_SO
+lapply (nexts_le h k d) #H
 @(le_to_lt_to_lt … H) //
 qed.
 
-axiom nexts_dec: ∀h,k1,k2. Decidable (∃l. (next h)^l k1 = k2).
+axiom nexts_dec: ∀h,k1,k2. Decidable (∃d. (next h)^d k1 = k2).
 
-axiom nexts_inj: ∀h,k,l1,l2. (next h)^l1 k = (next h)^l2 k → l1 = l2.
+axiom nexts_inj: ∀h,k,d1,d2. (next h)^d1 k = (next h)^d2 k → d1 = d2.