update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / ex2 / props.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/ex2/props.ma b/matita/matita/contribs/lambdadelta/basic_1/ex2/props.ma
index 4dfa6a5825e07d9e72bd27dea2c425caf64c00f0..42c2de64690174450e8494115675cbb8b967489e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/ex2/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/ex2/props.ma
@@ -14,15 +14,15 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/ex2/defs.ma".
+include "basic_1/ex2/defs.ma".
 
-include "Basic-1/nf2/defs.ma".
+include "basic_1/nf2/defs.ma".
 
-include "Basic-1/pr2/fwd.ma".
+include "basic_1/pr2/fwd.ma".
 
-include "Basic-1/arity/fwd.ma".
+include "basic_1/arity/fwd.ma".
 
-theorem ex2_nf2:
+lemma ex2_nf2:
  nf2 ex2_c ex2_t
 \def
  \lambda (t2: T).(\lambda (H: (pr2 (CSort O) (THead (Flat Appl) (TSort O) 
@@ -85,27 +85,27 @@ B).(\forall (u: T).(pr2 (CHead (CSort O) (Bind b) u) x1 x3))))).(let H6 \def
 (eq_ind T x2 (\lambda (t: T).(eq T t2 (THead (Bind Abbr) t x3))) H3 (TSort O) 
 (pr2_gen_sort (CSort O) x2 O H4)) in (eq_ind_r T (THead (Bind Abbr) (TSort O) 
 x3) (\lambda (t: T).(eq T (THead (Flat Appl) (TSort O) (TSort O)) t)) (let H7 
-\def (eq_ind T (TSort O) (\lambda (ee: T).(match ee in T return (\lambda (_: 
-T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | 
-(THead _ _ _) \Rightarrow False])) I (THead (Bind Abst) x0 x1) H2) in 
-(False_ind (eq T (THead (Flat Appl) (TSort O) (TSort O)) (THead (Bind Abbr) 
-(TSort O) x3)) H7)) t2 H6)))))))))) H1)) (\lambda (H1: (ex6_6 B T T T T T 
-(\lambda (b: B).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: 
-T).(\lambda (_: T).(not (eq B b Abst)))))))) (\lambda (b: B).(\lambda (y1: 
-T).(\lambda (z1: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(eq T 
-(TSort O) (THead (Bind b) y1 z1)))))))) (\lambda (b: B).(\lambda (_: 
-T).(\lambda (_: T).(\lambda (z2: T).(\lambda (u2: T).(\lambda (y2: T).(eq T 
-t2 (THead (Bind b) y2 (THead (Flat Appl) (lift (S O) O u2) z2))))))))) 
-(\lambda (_: B).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (u2: 
-T).(\lambda (_: T).(pr2 (CSort O) (TSort O) u2))))))) (\lambda (_: 
-B).(\lambda (y1: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda 
-(y2: T).(pr2 (CSort O) y1 y2))))))) (\lambda (b: B).(\lambda (_: T).(\lambda 
-(z1: T).(\lambda (z2: T).(\lambda (_: T).(\lambda (y2: T).(pr2 (CHead (CSort 
-O) (Bind b) y2) z1 z2))))))))).(ex6_6_ind B T T T T T (\lambda (b: 
-B).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda 
-(_: T).(not (eq B b Abst)))))))) (\lambda (b: B).(\lambda (y1: T).(\lambda 
-(z1: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(eq T (TSort O) 
-(THead (Bind b) y1 z1)))))))) (\lambda (b: B).(\lambda (_: T).(\lambda (_: 
+\def (eq_ind T (TSort O) (\lambda (ee: T).(match ee with [(TSort _) 
+\Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow 
+False])) I (THead (Bind Abst) x0 x1) H2) in (False_ind (eq T (THead (Flat 
+Appl) (TSort O) (TSort O)) (THead (Bind Abbr) (TSort O) x3)) H7)) t2 
+H6)))))))))) H1)) (\lambda (H1: (ex6_6 B T T T T T (\lambda (b: B).(\lambda 
+(_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(not 
+(eq B b Abst)))))))) (\lambda (b: B).(\lambda (y1: T).(\lambda (z1: 
+T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(eq T (TSort O) (THead 
+(Bind b) y1 z1)))))))) (\lambda (b: B).(\lambda (_: T).(\lambda (_: 
+T).(\lambda (z2: T).(\lambda (u2: T).(\lambda (y2: T).(eq T t2 (THead (Bind 
+b) y2 (THead (Flat Appl) (lift (S O) O u2) z2))))))))) (\lambda (_: 
+B).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (u2: T).(\lambda 
+(_: T).(pr2 (CSort O) (TSort O) u2))))))) (\lambda (_: B).(\lambda (y1: 
+T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (y2: T).(pr2 
+(CSort O) y1 y2))))))) (\lambda (b: B).(\lambda (_: T).(\lambda (z1: 
+T).(\lambda (z2: T).(\lambda (_: T).(\lambda (y2: T).(pr2 (CHead (CSort O) 
+(Bind b) y2) z1 z2))))))))).(ex6_6_ind B T T T T T (\lambda (b: B).(\lambda 
+(_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(not 
+(eq B b Abst)))))))) (\lambda (b: B).(\lambda (y1: T).(\lambda (z1: 
+T).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(eq T (TSort O) (THead 
+(Bind b) y1 z1)))))))) (\lambda (b: B).(\lambda (_: T).(\lambda (_: 
 T).(\lambda (z2: T).(\lambda (u2: T).(\lambda (y2: T).(eq T t2 (THead (Bind 
 b) y2 (THead (Flat Appl) (lift (S O) O u2) z2))))))))) (\lambda (_: 
 B).(\lambda (_: T).(\lambda (_: T).(\lambda (_: T).(\lambda (u2: T).(\lambda 
@@ -124,17 +124,13 @@ x5 (THead (Flat Appl) (lift (S O) O x4) x3)))).(\lambda (H5: (pr2 (CSort O)
 (Flat Appl) (lift (S O) O t) x3)))) H4 (TSort O) (pr2_gen_sort (CSort O) x4 O 
 H5)) in (eq_ind_r T (THead (Bind x0) x5 (THead (Flat Appl) (lift (S O) O 
 (TSort O)) x3)) (\lambda (t: T).(eq T (THead (Flat Appl) (TSort O) (TSort O)) 
-t)) (let H9 \def (eq_ind T (TSort O) (\lambda (ee: T).(match ee in T return 
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) 
-\Rightarrow False | (THead _ _ _) \Rightarrow False])) I (THead (Bind x0) x1 
-x2) H3) in (False_ind (eq T (THead (Flat Appl) (TSort O) (TSort O)) (THead 
-(Bind x0) x5 (THead (Flat Appl) (lift (S O) O (TSort O)) x3))) H9)) t2 
-H8))))))))))))))) H1)) H0))).
-(* COMMENTS
-Initial nodes: 1939
-END *)
+t)) (let H9 \def (eq_ind T (TSort O) (\lambda (ee: T).(match ee with [(TSort 
+_) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow 
+False])) I (THead (Bind x0) x1 x2) H3) in (False_ind (eq T (THead (Flat Appl) 
+(TSort O) (TSort O)) (THead (Bind x0) x5 (THead (Flat Appl) (lift (S O) O 
+(TSort O)) x3))) H9)) t2 H8))))))))))))))) H1)) H0))).
 
-theorem ex2_arity:
+lemma ex2_arity:
  \forall (g: G).(\forall (a: A).((arity g ex2_c ex2_t a) \to (\forall (P: 
 Prop).P)))
 \def
@@ -150,10 +146,7 @@ A).(\lambda (_: A).(leq g x a3))) (\lambda (_: A).(\lambda (a4: A).(leq g a
 a4))) (\lambda (a3: A).(\lambda (a4: A).(eq A (ASort O O) (AHead a3 a4)))) P 
 (\lambda (x0: A).(\lambda (x1: A).(\lambda (_: (leq g x x0)).(\lambda (_: 
 (leq g a x1)).(\lambda (H6: (eq A (ASort O O) (AHead x0 x1))).(let H7 \def 
-(eq_ind A (ASort O O) (\lambda (ee: A).(match ee in A return (\lambda (_: 
-A).Prop) with [(ASort _ _) \Rightarrow True | (AHead _ _) \Rightarrow 
-False])) I (AHead x0 x1) H6) in (False_ind P H7))))))) H3)))))) H0))))).
-(* COMMENTS
-Initial nodes: 289
-END *)
+(eq_ind A (ASort O O) (\lambda (ee: A).(match ee with [(ASort _ _) 
+\Rightarrow True | (AHead _ _) \Rightarrow False])) I (AHead x0 x1) H6) in 
+(False_ind P H7))))))) H3)))))) H0))))).