update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / csubc / drop1.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubc/drop1.ma b/matita/matita/contribs/lambdadelta/basic_1/csubc/drop1.ma
index 54465953f1126076256991a33861ecd1a38f82f0..32574ea29f7eb4b590182636c0304e4ac7de69ee 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/csubc/drop1.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubc/drop1.ma
@@ -16,96 +16,71 @@
 
 include "basic_1/csubc/drop.ma".
 
-theorem drop1_csubc_trans:
+lemma drop1_csubc_trans:
  \forall (g: G).(\forall (hds: PList).(\forall (c2: C).(\forall (e2: 
 C).((drop1 hds c2 e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C 
 (\lambda (c1: C).(drop1 hds c1 e1)) (\lambda (c1: C).(csubc g c2 c1)))))))))
 \def
- \lambda (g: G).(\lambda (hds: PList).(let TMP_3 \def (\lambda (p: 
-PList).(\forall (c2: C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1: 
-C).((csubc g e2 e1) \to (let TMP_1 \def (\lambda (c1: C).(drop1 p c1 e1)) in 
-(let TMP_2 \def (\lambda (c1: C).(csubc g c2 c1)) in (ex2 C TMP_1 
-TMP_2))))))))) in (let TMP_8 \def (\lambda (c2: C).(\lambda (e2: C).(\lambda 
-(H: (drop1 PNil c2 e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e2 e1)).(let 
-H_y \def (drop1_gen_pnil c2 e2 H) in (let TMP_4 \def (\lambda (c: C).(csubc g 
-c e1)) in (let H1 \def (eq_ind_r C e2 TMP_4 H0 c2 H_y) in (let TMP_5 \def 
-(\lambda (c1: C).(drop1 PNil c1 e1)) in (let TMP_6 \def (\lambda (c1: 
-C).(csubc g c2 c1)) in (let TMP_7 \def (drop1_nil e1) in (ex_intro2 C TMP_5 
-TMP_6 e1 TMP_7 H1)))))))))))) in (let TMP_34 \def (\lambda (n: nat).(\lambda 
-(n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c2: C).(\forall (e2: 
-C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C (\lambda 
-(c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c2 c1)))))))))).(\lambda 
-(c2: C).(\lambda (e2: C).(\lambda (H0: (drop1 (PCons n n0 p) c2 e2)).(\lambda 
-(e1: C).(\lambda (H1: (csubc g e2 e1)).(let H_x \def (drop1_gen_pcons c2 e2 p 
-n n0 H0) in (let H2 \def H_x in (let TMP_9 \def (\lambda (c3: C).(drop n n0 
-c2 c3)) in (let TMP_10 \def (\lambda (c3: C).(drop1 p c3 e2)) in (let TMP_12 
-\def (\lambda (c1: C).(let TMP_11 \def (PCons n n0 p) in (drop1 TMP_11 c1 
-e1))) in (let TMP_13 \def (\lambda (c1: C).(csubc g c2 c1)) in (let TMP_14 
-\def (ex2 C TMP_12 TMP_13) in (let TMP_33 \def (\lambda (x: C).(\lambda (H3: 
-(drop n n0 c2 x)).(\lambda (H4: (drop1 p x e2)).(let H_x0 \def (H x e2 H4 e1 
-H1) in (let H5 \def H_x0 in (let TMP_15 \def (\lambda (c1: C).(drop1 p c1 
-e1)) in (let TMP_16 \def (\lambda (c1: C).(csubc g x c1)) in (let TMP_18 \def 
-(\lambda (c1: C).(let TMP_17 \def (PCons n n0 p) in (drop1 TMP_17 c1 e1))) in 
-(let TMP_19 \def (\lambda (c1: C).(csubc g c2 c1)) in (let TMP_20 \def (ex2 C 
-TMP_18 TMP_19) in (let TMP_32 \def (\lambda (x0: C).(\lambda (H6: (drop1 p x0 
-e1)).(\lambda (H7: (csubc g x x0)).(let H_x1 \def (drop_csubc_trans g c2 x n0 
-n H3 x0 H7) in (let H8 \def H_x1 in (let TMP_21 \def (\lambda (c1: C).(drop n 
-n0 c1 x0)) in (let TMP_22 \def (\lambda (c1: C).(csubc g c2 c1)) in (let 
-TMP_24 \def (\lambda (c1: C).(let TMP_23 \def (PCons n n0 p) in (drop1 TMP_23 
-c1 e1))) in (let TMP_25 \def (\lambda (c1: C).(csubc g c2 c1)) in (let TMP_26 
-\def (ex2 C TMP_24 TMP_25) in (let TMP_31 \def (\lambda (x1: C).(\lambda (H9: 
-(drop n n0 x1 x0)).(\lambda (H10: (csubc g c2 x1)).(let TMP_28 \def (\lambda 
-(c1: C).(let TMP_27 \def (PCons n n0 p) in (drop1 TMP_27 c1 e1))) in (let 
-TMP_29 \def (\lambda (c1: C).(csubc g c2 c1)) in (let TMP_30 \def (drop1_cons 
-x1 x0 n n0 H9 e1 p H6) in (ex_intro2 C TMP_28 TMP_29 x1 TMP_30 H10))))))) in 
-(ex2_ind C TMP_21 TMP_22 TMP_26 TMP_31 H8)))))))))))) in (ex2_ind C TMP_15 
-TMP_16 TMP_20 TMP_32 H5)))))))))))) in (ex2_ind C TMP_9 TMP_10 TMP_14 TMP_33 
-H2)))))))))))))))))) in (PList_ind TMP_3 TMP_8 TMP_34 hds))))).
+ \lambda (g: G).(\lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall 
+(c2: C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e2 
+e1) \to (ex2 C (\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c2 
+c1))))))))) (\lambda (c2: C).(\lambda (e2: C).(\lambda (H: (drop1 PNil c2 
+e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e2 e1)).(let H_y \def 
+(drop1_gen_pnil c2 e2 H) in (let H1 \def (eq_ind_r C e2 (\lambda (c: 
+C).(csubc g c e1)) H0 c2 H_y) in (ex_intro2 C (\lambda (c1: C).(drop1 PNil c1 
+e1)) (\lambda (c1: C).(csubc g c2 c1)) e1 (drop1_nil e1) H1)))))))) (\lambda 
+(n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c2: 
+C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e2 e1) 
+\to (ex2 C (\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c2 
+c1)))))))))).(\lambda (c2: C).(\lambda (e2: C).(\lambda (H0: (drop1 (PCons n 
+n0 p) c2 e2)).(\lambda (e1: C).(\lambda (H1: (csubc g e2 e1)).(let H_x \def 
+(drop1_gen_pcons c2 e2 p n n0 H0) in (let H2 \def H_x in (ex2_ind C (\lambda 
+(c3: C).(drop n n0 c2 c3)) (\lambda (c3: C).(drop1 p c3 e2)) (ex2 C (\lambda 
+(c1: C).(drop1 (PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c2 c1))) 
+(\lambda (x: C).(\lambda (H3: (drop n n0 c2 x)).(\lambda (H4: (drop1 p x 
+e2)).(let H_x0 \def (H x e2 H4 e1 H1) in (let H5 \def H_x0 in (ex2_ind C 
+(\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g x c1)) (ex2 C 
+(\lambda (c1: C).(drop1 (PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c2 
+c1))) (\lambda (x0: C).(\lambda (H6: (drop1 p x0 e1)).(\lambda (H7: (csubc g 
+x x0)).(let H_x1 \def (drop_csubc_trans g c2 x n0 n H3 x0 H7) in (let H8 \def 
+H_x1 in (ex2_ind C (\lambda (c1: C).(drop n n0 c1 x0)) (\lambda (c1: 
+C).(csubc g c2 c1)) (ex2 C (\lambda (c1: C).(drop1 (PCons n n0 p) c1 e1)) 
+(\lambda (c1: C).(csubc g c2 c1))) (\lambda (x1: C).(\lambda (H9: (drop n n0 
+x1 x0)).(\lambda (H10: (csubc g c2 x1)).(ex_intro2 C (\lambda (c1: C).(drop1 
+(PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c2 c1)) x1 (drop1_cons x1 x0 
+n n0 H9 e1 p H6) H10)))) H8)))))) H5)))))) H2)))))))))))) hds)).
 
-theorem csubc_drop1_conf_rev:
+lemma csubc_drop1_conf_rev:
  \forall (g: G).(\forall (hds: PList).(\forall (c2: C).(\forall (e2: 
 C).((drop1 hds c2 e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C 
 (\lambda (c1: C).(drop1 hds c1 e1)) (\lambda (c1: C).(csubc g c1 c2)))))))))
 \def
- \lambda (g: G).(\lambda (hds: PList).(let TMP_3 \def (\lambda (p: 
-PList).(\forall (c2: C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1: 
-C).((csubc g e1 e2) \to (let TMP_1 \def (\lambda (c1: C).(drop1 p c1 e1)) in 
-(let TMP_2 \def (\lambda (c1: C).(csubc g c1 c2)) in (ex2 C TMP_1 
-TMP_2))))))))) in (let TMP_8 \def (\lambda (c2: C).(\lambda (e2: C).(\lambda 
-(H: (drop1 PNil c2 e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e1 e2)).(let 
-H_y \def (drop1_gen_pnil c2 e2 H) in (let TMP_4 \def (\lambda (c: C).(csubc g 
-e1 c)) in (let H1 \def (eq_ind_r C e2 TMP_4 H0 c2 H_y) in (let TMP_5 \def 
-(\lambda (c1: C).(drop1 PNil c1 e1)) in (let TMP_6 \def (\lambda (c1: 
-C).(csubc g c1 c2)) in (let TMP_7 \def (drop1_nil e1) in (ex_intro2 C TMP_5 
-TMP_6 e1 TMP_7 H1)))))))))))) in (let TMP_34 \def (\lambda (n: nat).(\lambda 
-(n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c2: C).(\forall (e2: 
-C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C (\lambda 
-(c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c1 c2)))))))))).(\lambda 
-(c2: C).(\lambda (e2: C).(\lambda (H0: (drop1 (PCons n n0 p) c2 e2)).(\lambda 
-(e1: C).(\lambda (H1: (csubc g e1 e2)).(let H_x \def (drop1_gen_pcons c2 e2 p 
-n n0 H0) in (let H2 \def H_x in (let TMP_9 \def (\lambda (c3: C).(drop n n0 
-c2 c3)) in (let TMP_10 \def (\lambda (c3: C).(drop1 p c3 e2)) in (let TMP_12 
-\def (\lambda (c1: C).(let TMP_11 \def (PCons n n0 p) in (drop1 TMP_11 c1 
-e1))) in (let TMP_13 \def (\lambda (c1: C).(csubc g c1 c2)) in (let TMP_14 
-\def (ex2 C TMP_12 TMP_13) in (let TMP_33 \def (\lambda (x: C).(\lambda (H3: 
-(drop n n0 c2 x)).(\lambda (H4: (drop1 p x e2)).(let H_x0 \def (H x e2 H4 e1 
-H1) in (let H5 \def H_x0 in (let TMP_15 \def (\lambda (c1: C).(drop1 p c1 
-e1)) in (let TMP_16 \def (\lambda (c1: C).(csubc g c1 x)) in (let TMP_18 \def 
-(\lambda (c1: C).(let TMP_17 \def (PCons n n0 p) in (drop1 TMP_17 c1 e1))) in 
-(let TMP_19 \def (\lambda (c1: C).(csubc g c1 c2)) in (let TMP_20 \def (ex2 C 
-TMP_18 TMP_19) in (let TMP_32 \def (\lambda (x0: C).(\lambda (H6: (drop1 p x0 
-e1)).(\lambda (H7: (csubc g x0 x)).(let H_x1 \def (csubc_drop_conf_rev g c2 x 
-n0 n H3 x0 H7) in (let H8 \def H_x1 in (let TMP_21 \def (\lambda (c1: 
-C).(drop n n0 c1 x0)) in (let TMP_22 \def (\lambda (c1: C).(csubc g c1 c2)) 
-in (let TMP_24 \def (\lambda (c1: C).(let TMP_23 \def (PCons n n0 p) in 
-(drop1 TMP_23 c1 e1))) in (let TMP_25 \def (\lambda (c1: C).(csubc g c1 c2)) 
-in (let TMP_26 \def (ex2 C TMP_24 TMP_25) in (let TMP_31 \def (\lambda (x1: 
-C).(\lambda (H9: (drop n n0 x1 x0)).(\lambda (H10: (csubc g x1 c2)).(let 
-TMP_28 \def (\lambda (c1: C).(let TMP_27 \def (PCons n n0 p) in (drop1 TMP_27 
-c1 e1))) in (let TMP_29 \def (\lambda (c1: C).(csubc g c1 c2)) in (let TMP_30 
-\def (drop1_cons x1 x0 n n0 H9 e1 p H6) in (ex_intro2 C TMP_28 TMP_29 x1 
-TMP_30 H10))))))) in (ex2_ind C TMP_21 TMP_22 TMP_26 TMP_31 H8)))))))))))) in 
-(ex2_ind C TMP_15 TMP_16 TMP_20 TMP_32 H5)))))))))))) in (ex2_ind C TMP_9 
-TMP_10 TMP_14 TMP_33 H2)))))))))))))))))) in (PList_ind TMP_3 TMP_8 TMP_34 
-hds))))).
+ \lambda (g: G).(\lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall 
+(c2: C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e1 
+e2) \to (ex2 C (\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c1 
+c2))))))))) (\lambda (c2: C).(\lambda (e2: C).(\lambda (H: (drop1 PNil c2 
+e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e1 e2)).(let H_y \def 
+(drop1_gen_pnil c2 e2 H) in (let H1 \def (eq_ind_r C e2 (\lambda (c: 
+C).(csubc g e1 c)) H0 c2 H_y) in (ex_intro2 C (\lambda (c1: C).(drop1 PNil c1 
+e1)) (\lambda (c1: C).(csubc g c1 c2)) e1 (drop1_nil e1) H1)))))))) (\lambda 
+(n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c2: 
+C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e1 e2) 
+\to (ex2 C (\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c1 
+c2)))))))))).(\lambda (c2: C).(\lambda (e2: C).(\lambda (H0: (drop1 (PCons n 
+n0 p) c2 e2)).(\lambda (e1: C).(\lambda (H1: (csubc g e1 e2)).(let H_x \def 
+(drop1_gen_pcons c2 e2 p n n0 H0) in (let H2 \def H_x in (ex2_ind C (\lambda 
+(c3: C).(drop n n0 c2 c3)) (\lambda (c3: C).(drop1 p c3 e2)) (ex2 C (\lambda 
+(c1: C).(drop1 (PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c1 c2))) 
+(\lambda (x: C).(\lambda (H3: (drop n n0 c2 x)).(\lambda (H4: (drop1 p x 
+e2)).(let H_x0 \def (H x e2 H4 e1 H1) in (let H5 \def H_x0 in (ex2_ind C 
+(\lambda (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c1 x)) (ex2 C 
+(\lambda (c1: C).(drop1 (PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c1 
+c2))) (\lambda (x0: C).(\lambda (H6: (drop1 p x0 e1)).(\lambda (H7: (csubc g 
+x0 x)).(let H_x1 \def (csubc_drop_conf_rev g c2 x n0 n H3 x0 H7) in (let H8 
+\def H_x1 in (ex2_ind C (\lambda (c1: C).(drop n n0 c1 x0)) (\lambda (c1: 
+C).(csubc g c1 c2)) (ex2 C (\lambda (c1: C).(drop1 (PCons n n0 p) c1 e1)) 
+(\lambda (c1: C).(csubc g c1 c2))) (\lambda (x1: C).(\lambda (H9: (drop n n0 
+x1 x0)).(\lambda (H10: (csubc g x1 c2)).(ex_intro2 C (\lambda (c1: C).(drop1 
+(PCons n n0 p) c1 e1)) (\lambda (c1: C).(csubc g c1 c2)) x1 (drop1_cons x1 x0 
+n n0 H9 e1 p H6) H10)))) H8)))))) H5)))))) H2)))))))))))) hds)).