update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / ground_1 / types / defs.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_1/types/defs.ma b/matita/matita/contribs/lambdadelta/ground_1/types/defs.ma
index f94969d8852e05475127411893e77b05668ae816..3a7dadb6486f9df599453bcdeb05267476b121cd 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_1/types/defs.ma
+++ b/matita/matita/contribs/lambdadelta/ground_1/types/defs.ma
@@ -14,7 +14,7 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Ground-1/preamble.ma".
+include "ground_1/preamble.ma".
 
 inductive and3 (P0: Prop) (P1: Prop) (P2: Prop): Prop \def
 | and3_intro: P0 \to (P1 \to (P2 \to (and3 P0 P1 P2))).
@@ -46,122 +46,124 @@ inductive or5 (P0: Prop) (P1: Prop) (P2: Prop) (P3: Prop) (P4: Prop): Prop
 | or5_intro3: P3 \to (or5 P0 P1 P2 P3 P4)
 | or5_intro4: P4 \to (or5 P0 P1 P2 P3 P4).
 
-inductive ex3 (A0: Set) (P0: A0 \to Prop) (P1: A0 \to Prop) (P2: A0 \to 
+inductive ex3 (A0: Type[0]) (P0: A0 \to Prop) (P1: A0 \to Prop) (P2: A0 \to 
 Prop): Prop \def
 | ex3_intro: \forall (x0: A0).((P0 x0) \to ((P1 x0) \to ((P2 x0) \to (ex3 A0 
 P0 P1 P2)))).
 
-inductive ex4 (A0: Set) (P0: A0 \to Prop) (P1: A0 \to Prop) (P2: A0 \to Prop) 
-(P3: A0 \to Prop): Prop \def
+inductive ex4 (A0: Type[0]) (P0: A0 \to Prop) (P1: A0 \to Prop) (P2: A0 \to 
+Prop) (P3: A0 \to Prop): Prop \def
 | ex4_intro: \forall (x0: A0).((P0 x0) \to ((P1 x0) \to ((P2 x0) \to ((P3 x0) 
 \to (ex4 A0 P0 P1 P2 P3))))).
 
-inductive ex_2 (A0: Set) (A1: Set) (P0: A0 \to (A1 \to Prop)): Prop \def
+inductive ex_2 (A0: Type[0]) (A1: Type[0]) (P0: A0 \to (A1 \to Prop)): Prop 
+\def
 | ex_2_intro: \forall (x0: A0).(\forall (x1: A1).((P0 x0 x1) \to (ex_2 A0 A1 
 P0))).
 
-inductive ex2_2 (A0: Set) (A1: Set) (P0: A0 \to (A1 \to Prop)) (P1: A0 \to 
-(A1 \to Prop)): Prop \def
+inductive ex2_2 (A0: Type[0]) (A1: Type[0]) (P0: A0 \to (A1 \to Prop)) (P1: 
+A0 \to (A1 \to Prop)): Prop \def
 | ex2_2_intro: \forall (x0: A0).(\forall (x1: A1).((P0 x0 x1) \to ((P1 x0 x1) 
 \to (ex2_2 A0 A1 P0 P1)))).
 
-inductive ex3_2 (A0: Set) (A1: Set) (P0: A0 \to (A1 \to Prop)) (P1: A0 \to 
-(A1 \to Prop)) (P2: A0 \to (A1 \to Prop)): Prop \def
+inductive ex3_2 (A0: Type[0]) (A1: Type[0]) (P0: A0 \to (A1 \to Prop)) (P1: 
+A0 \to (A1 \to Prop)) (P2: A0 \to (A1 \to Prop)): Prop \def
 | ex3_2_intro: \forall (x0: A0).(\forall (x1: A1).((P0 x0 x1) \to ((P1 x0 x1) 
 \to ((P2 x0 x1) \to (ex3_2 A0 A1 P0 P1 P2))))).
 
-inductive ex4_2 (A0: Set) (A1: Set) (P0: A0 \to (A1 \to Prop)) (P1: A0 \to 
-(A1 \to Prop)) (P2: A0 \to (A1 \to Prop)) (P3: A0 \to (A1 \to Prop)): Prop 
-\def
+inductive ex4_2 (A0: Type[0]) (A1: Type[0]) (P0: A0 \to (A1 \to Prop)) (P1: 
+A0 \to (A1 \to Prop)) (P2: A0 \to (A1 \to Prop)) (P3: A0 \to (A1 \to Prop)): 
+Prop \def
 | ex4_2_intro: \forall (x0: A0).(\forall (x1: A1).((P0 x0 x1) \to ((P1 x0 x1) 
 \to ((P2 x0 x1) \to ((P3 x0 x1) \to (ex4_2 A0 A1 P0 P1 P2 P3)))))).
 
-inductive ex_3 (A0: Set) (A1: Set) (A2: Set) (P0: A0 \to (A1 \to (A2 \to 
-Prop))): Prop \def
+inductive ex_3 (A0: Type[0]) (A1: Type[0]) (A2: Type[0]) (P0: A0 \to (A1 \to 
+(A2 \to Prop))): Prop \def
 | ex_3_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).((P0 x0 x1 
 x2) \to (ex_3 A0 A1 A2 P0)))).
 
-inductive ex2_3 (A0: Set) (A1: Set) (A2: Set) (P0: A0 \to (A1 \to (A2 \to 
-Prop))) (P1: A0 \to (A1 \to (A2 \to Prop))): Prop \def
+inductive ex2_3 (A0: Type[0]) (A1: Type[0]) (A2: Type[0]) (P0: A0 \to (A1 \to 
+(A2 \to Prop))) (P1: A0 \to (A1 \to (A2 \to Prop))): Prop \def
 | ex2_3_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).((P0 x0 
 x1 x2) \to ((P1 x0 x1 x2) \to (ex2_3 A0 A1 A2 P0 P1))))).
 
-inductive ex3_3 (A0: Set) (A1: Set) (A2: Set) (P0: A0 \to (A1 \to (A2 \to 
-Prop))) (P1: A0 \to (A1 \to (A2 \to Prop))) (P2: A0 \to (A1 \to (A2 \to 
-Prop))): Prop \def
+inductive ex3_3 (A0: Type[0]) (A1: Type[0]) (A2: Type[0]) (P0: A0 \to (A1 \to 
+(A2 \to Prop))) (P1: A0 \to (A1 \to (A2 \to Prop))) (P2: A0 \to (A1 \to (A2 
+\to Prop))): Prop \def
 | ex3_3_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).((P0 x0 
 x1 x2) \to ((P1 x0 x1 x2) \to ((P2 x0 x1 x2) \to (ex3_3 A0 A1 A2 P0 P1 
 P2)))))).
 
-inductive ex4_3 (A0: Set) (A1: Set) (A2: Set) (P0: A0 \to (A1 \to (A2 \to 
-Prop))) (P1: A0 \to (A1 \to (A2 \to Prop))) (P2: A0 \to (A1 \to (A2 \to 
-Prop))) (P3: A0 \to (A1 \to (A2 \to Prop))): Prop \def
+inductive ex4_3 (A0: Type[0]) (A1: Type[0]) (A2: Type[0]) (P0: A0 \to (A1 \to 
+(A2 \to Prop))) (P1: A0 \to (A1 \to (A2 \to Prop))) (P2: A0 \to (A1 \to (A2 
+\to Prop))) (P3: A0 \to (A1 \to (A2 \to Prop))): Prop \def
 | ex4_3_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).((P0 x0 
 x1 x2) \to ((P1 x0 x1 x2) \to ((P2 x0 x1 x2) \to ((P3 x0 x1 x2) \to (ex4_3 A0 
 A1 A2 P0 P1 P2 P3))))))).
 
-inductive ex5_3 (A0: Set) (A1: Set) (A2: Set) (P0: A0 \to (A1 \to (A2 \to 
-Prop))) (P1: A0 \to (A1 \to (A2 \to Prop))) (P2: A0 \to (A1 \to (A2 \to 
-Prop))) (P3: A0 \to (A1 \to (A2 \to Prop))) (P4: A0 \to (A1 \to (A2 \to 
+inductive ex5_3 (A0: Type[0]) (A1: Type[0]) (A2: Type[0]) (P0: A0 \to (A1 \to 
+(A2 \to Prop))) (P1: A0 \to (A1 \to (A2 \to Prop))) (P2: A0 \to (A1 \to (A2 
+\to Prop))) (P3: A0 \to (A1 \to (A2 \to Prop))) (P4: A0 \to (A1 \to (A2 \to 
 Prop))): Prop \def
 | ex5_3_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).((P0 x0 
 x1 x2) \to ((P1 x0 x1 x2) \to ((P2 x0 x1 x2) \to ((P3 x0 x1 x2) \to ((P4 x0 
 x1 x2) \to (ex5_3 A0 A1 A2 P0 P1 P2 P3 P4)))))))).
 
-inductive ex3_4 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (P0: A0 \to (A1 \to 
-(A2 \to (A3 \to Prop)))) (P1: A0 \to (A1 \to (A2 \to (A3 \to Prop)))) (P2: A0 
-\to (A1 \to (A2 \to (A3 \to Prop)))): Prop \def
+inductive ex3_4 (A0: Type[0]) (A1: Type[0]) (A2: Type[0]) (A3: Type[0]) (P0: 
+A0 \to (A1 \to (A2 \to (A3 \to Prop)))) (P1: A0 \to (A1 \to (A2 \to (A3 \to 
+Prop)))) (P2: A0 \to (A1 \to (A2 \to (A3 \to Prop)))): Prop \def
 | ex3_4_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall 
 (x3: A3).((P0 x0 x1 x2 x3) \to ((P1 x0 x1 x2 x3) \to ((P2 x0 x1 x2 x3) \to 
 (ex3_4 A0 A1 A2 A3 P0 P1 P2))))))).
 
-inductive ex4_4 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (P0: A0 \to (A1 \to 
-(A2 \to (A3 \to Prop)))) (P1: A0 \to (A1 \to (A2 \to (A3 \to Prop)))) (P2: A0 
-\to (A1 \to (A2 \to (A3 \to Prop)))) (P3: A0 \to (A1 \to (A2 \to (A3 \to 
-Prop)))): Prop \def
+inductive ex4_4 (A0: Type[0]) (A1: Type[0]) (A2: Type[0]) (A3: Type[0]) (P0: 
+A0 \to (A1 \to (A2 \to (A3 \to Prop)))) (P1: A0 \to (A1 \to (A2 \to (A3 \to 
+Prop)))) (P2: A0 \to (A1 \to (A2 \to (A3 \to Prop)))) (P3: A0 \to (A1 \to (A2 
+\to (A3 \to Prop)))): Prop \def
 | ex4_4_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall 
 (x3: A3).((P0 x0 x1 x2 x3) \to ((P1 x0 x1 x2 x3) \to ((P2 x0 x1 x2 x3) \to 
 ((P3 x0 x1 x2 x3) \to (ex4_4 A0 A1 A2 A3 P0 P1 P2 P3)))))))).
 
-inductive ex4_5 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (A4: Set) (P0: A0 \to 
-(A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P1: A0 \to (A1 \to (A2 \to (A3 \to 
-(A4 \to Prop))))) (P2: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P3: 
-A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))): Prop \def
+inductive ex4_5 (A0: Type[0]) (A1: Type[0]) (A2: Type[0]) (A3: Type[0]) (A4: 
+Type[0]) (P0: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P1: A0 \to 
+(A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P2: A0 \to (A1 \to (A2 \to (A3 \to 
+(A4 \to Prop))))) (P3: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))): Prop 
+\def
 | ex4_5_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall 
 (x3: A3).(\forall (x4: A4).((P0 x0 x1 x2 x3 x4) \to ((P1 x0 x1 x2 x3 x4) \to 
 ((P2 x0 x1 x2 x3 x4) \to ((P3 x0 x1 x2 x3 x4) \to (ex4_5 A0 A1 A2 A3 A4 P0 P1 
 P2 P3))))))))).
 
-inductive ex5_5 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (A4: Set) (P0: A0 \to 
-(A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P1: A0 \to (A1 \to (A2 \to (A3 \to 
-(A4 \to Prop))))) (P2: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P3: 
-A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P4: A0 \to (A1 \to (A2 \to 
-(A3 \to (A4 \to Prop))))): Prop \def
+inductive ex5_5 (A0: Type[0]) (A1: Type[0]) (A2: Type[0]) (A3: Type[0]) (A4: 
+Type[0]) (P0: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P1: A0 \to 
+(A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P2: A0 \to (A1 \to (A2 \to (A3 \to 
+(A4 \to Prop))))) (P3: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))) (P4: 
+A0 \to (A1 \to (A2 \to (A3 \to (A4 \to Prop))))): Prop \def
 | ex5_5_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall 
 (x3: A3).(\forall (x4: A4).((P0 x0 x1 x2 x3 x4) \to ((P1 x0 x1 x2 x3 x4) \to 
 ((P2 x0 x1 x2 x3 x4) \to ((P3 x0 x1 x2 x3 x4) \to ((P4 x0 x1 x2 x3 x4) \to 
 (ex5_5 A0 A1 A2 A3 A4 P0 P1 P2 P3 P4)))))))))).
 
-inductive ex6_6 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (A4: Set) (A5: Set) 
-(P0: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to Prop)))))) (P1: A0 \to 
-(A1 \to (A2 \to (A3 \to (A4 \to (A5 \to Prop)))))) (P2: A0 \to (A1 \to (A2 
-\to (A3 \to (A4 \to (A5 \to Prop)))))) (P3: A0 \to (A1 \to (A2 \to (A3 \to 
-(A4 \to (A5 \to Prop)))))) (P4: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 
-\to Prop)))))) (P5: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to 
-Prop)))))): Prop \def
+inductive ex6_6 (A0: Type[0]) (A1: Type[0]) (A2: Type[0]) (A3: Type[0]) (A4: 
+Type[0]) (A5: Type[0]) (P0: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to 
+Prop)))))) (P1: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to Prop)))))) 
+(P2: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to Prop)))))) (P3: A0 \to 
+(A1 \to (A2 \to (A3 \to (A4 \to (A5 \to Prop)))))) (P4: A0 \to (A1 \to (A2 
+\to (A3 \to (A4 \to (A5 \to Prop)))))) (P5: A0 \to (A1 \to (A2 \to (A3 \to 
+(A4 \to (A5 \to Prop)))))): Prop \def
 | ex6_6_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall 
 (x3: A3).(\forall (x4: A4).(\forall (x5: A5).((P0 x0 x1 x2 x3 x4 x5) \to ((P1 
 x0 x1 x2 x3 x4 x5) \to ((P2 x0 x1 x2 x3 x4 x5) \to ((P3 x0 x1 x2 x3 x4 x5) 
 \to ((P4 x0 x1 x2 x3 x4 x5) \to ((P5 x0 x1 x2 x3 x4 x5) \to (ex6_6 A0 A1 A2 
 A3 A4 A5 P0 P1 P2 P3 P4 P5)))))))))))).
 
-inductive ex6_7 (A0: Set) (A1: Set) (A2: Set) (A3: Set) (A4: Set) (A5: Set) 
-(A6: Set) (P0: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to 
-Prop))))))) (P1: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to 
-Prop))))))) (P2: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to 
-Prop))))))) (P3: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to 
-Prop))))))) (P4: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to 
-Prop))))))) (P5: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to 
+inductive ex6_7 (A0: Type[0]) (A1: Type[0]) (A2: Type[0]) (A3: Type[0]) (A4: 
+Type[0]) (A5: Type[0]) (A6: Type[0]) (P0: A0 \to (A1 \to (A2 \to (A3 \to (A4 
+\to (A5 \to (A6 \to Prop))))))) (P1: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to 
+(A5 \to (A6 \to Prop))))))) (P2: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 
+\to (A6 \to Prop))))))) (P3: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to 
+(A6 \to Prop))))))) (P4: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 
+\to Prop))))))) (P5: A0 \to (A1 \to (A2 \to (A3 \to (A4 \to (A5 \to (A6 \to 
 Prop))))))): Prop \def
 | ex6_7_intro: \forall (x0: A0).(\forall (x1: A1).(\forall (x2: A2).(\forall 
 (x3: A3).(\forall (x4: A4).(\forall (x5: A5).(\forall (x6: A6).((P0 x0 x1 x2