Progress.

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / csn_alt.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/csn_alt.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/csn_alt.ma
index 6b4b61ae631ce8062e1c343dff77c922d0dac49b..980b4b7002b71eb2fc878321b86d385476194dd0 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/csn_alt.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/csn_alt.ma
@@ -28,7 +28,7 @@ interpretation
 
 lemma csna_ind: ∀L. ∀R:predicate term.
                 (∀T1. L ⊢ ⬇⬇* T1 →
-                      (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → False) → R T2) → R T1
+                      (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) → R T2) → R T1
                 ) →
                 ∀T. L ⊢ ⬇⬇* T → R T.
 #L #R #H0 #T1 #H elim H -T1 #T1 #HT1 #IHT1
@@ -39,13 +39,11 @@ qed-.
 
 (* Basic_1: was: sn3_intro *)
 lemma csna_intro: ∀L,T1.
-                  (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → False) → L ⊢ ⬇⬇* T2) → L ⊢ ⬇⬇* T1.
-#L #T1 #H
-@(SN_intro … H)
-qed.
+                  (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) → L ⊢ ⬇⬇* T2) → L ⊢ ⬇⬇* T1.
+/4 width=1/ qed.
 
 fact csna_intro_aux: ∀L,T1.
-                     (∀T,T2. L ⊢ T ➡* T2 → T1 = T → (T1 = T2 → False) → L ⊢ ⬇⬇* T2) → L ⊢ ⬇⬇* T1.
+                     (∀T,T2. L ⊢ T ➡* T2 → T1 = T → (T1 = T2 → ⊥) → L ⊢ ⬇⬇* T2) → L ⊢ ⬇⬇* T1.
 /4 width=3/ qed-.
 
 (* Basic_1: was: sn3_pr3_trans (old version) *)
@@ -59,7 +57,7 @@ qed.
 
 (* Basic_1: was: sn3_pr2_intro (old version) *)
 lemma csna_intro_cpr: ∀L,T1.
-                      (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → False) → L ⊢ ⬇⬇* T2) →
+                      (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) → L ⊢ ⬇⬇* T2) →
                       L ⊢ ⬇⬇* T1.
 #L #T1 #H
 @csna_intro_aux #T #T2 #H @(cprs_ind_dx … H) -T
@@ -91,7 +89,7 @@ lemma csn_cprs_trans: ∀L,T1. L ⊢ ⬇* T1 → ∀T2. L ⊢ T1 ➡* T2 → L 
 
 lemma csn_ind_alt: ∀L. ∀R:predicate term.
                    (∀T1. L ⊢ ⬇* T1 →
-                         (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → False) → R T2) → R T1
+                         (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) → R T2) → R T1
                    ) →
                    ∀T. L ⊢ ⬇* T → R T.
 #L #R #H0 #T1 #H @(csna_ind … (csn_csna … H)) -T1 #T1 #HT1 #IHT1