update in basic_2 and apps_2

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / examples / ex_fpbg_refl.ma

diff --git a/matita/matita/contribs/lambdadelta/apps_2/examples/ex_fpbg_refl.ma b/matita/matita/contribs/lambdadelta/apps_2/examples/ex_fpbg_refl.ma
index 232f9e8a7385abd28434cf61c94786d707d9cd7d..8a459a0be7b90e0925f4b8703ea35a4079f80aee 100644 (file)
--- a/matita/matita/contribs/lambdadelta/apps_2/examples/ex_fpbg_refl.ma
+++ b/matita/matita/contribs/lambdadelta/apps_2/examples/ex_fpbg_refl.ma
@@ -32,17 +32,17 @@ definition ApplOmega4 (s0) (s): term ≝ ⓐ⋆s.(ApplOmega1 s0 s).
 
 (* Basic properties *********************************************************)
 
-lemma ApplDelta_lifts (f:rtmap) (s0) (s):
-                      ⇧*[f] (ApplDelta s0 s) ≘ (ApplDelta s0 s).
+lemma ApplDelta_lifts (f) (s0) (s):
+      ⇧*[f] (ApplDelta s0 s) ≘ (ApplDelta s0 s).
 /5 width=1 by lifts_sort, lifts_lref, lifts_bind, lifts_flat/ qed.
 
-lemma cpr_ApplOmega_12 (h) (G) (L) (s0) (s): ❪G,L❫ ⊢ ApplOmega1 s0 s ➡[h] ApplOmega2 s0 s.
+lemma cpr_ApplOmega_12 (h) (G) (L) (s0) (s): ❪G,L❫ ⊢ ApplOmega1 s0 s ➡[h,0] ApplOmega2 s0 s.
 /2 width=1 by cpm_beta/ qed.
 
-lemma cpr_ApplOmega_23 (h) (G) (L) (s0) (s): ❪G,L❫ ⊢ ApplOmega2 s0 s ➡[h] ApplOmega3 s0 s.
+lemma cpr_ApplOmega_23 (h) (G) (L) (s0) (s): ❪G,L❫ ⊢ ApplOmega2 s0 s ➡[h,0] ApplOmega3 s0 s.
 /6 width=3 by cpm_eps, cpm_appl, cpm_bind, cpm_delta, ApplDelta_lifts/ qed.
 
-lemma cpr_ApplOmega_34 (h) (G) (L) (s0) (s): ❪G,L❫ ⊢ ApplOmega3 s0 s ➡[h] ApplOmega4 s0 s.
+lemma cpr_ApplOmega_34 (h) (G) (L) (s0) (s): ❪G,L❫ ⊢ ApplOmega3 s0 s ➡[h,0] ApplOmega4 s0 s.
 /4 width=3 by cpm_zeta, ApplDelta_lifts, lifts_sort, lifts_flat/ qed.
 
 lemma cpxs_ApplOmega_14 (h) (G) (L) (s0) (s): ❪G,L❫ ⊢ ApplOmega1 s0 s ⬈*[h] ApplOmega4 s0 s.