update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / fsubst0 / fwd.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/fsubst0/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/fsubst0/fwd.ma
index f43d06c9416a9b3787c2cdc09b0649c026f4b676..59ca03b0bd5b69a76d19e2e09d2bd65d3bd91d8e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/fsubst0/fwd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/fsubst0/fwd.ma
@@ -16,7 +16,7 @@
 
 include "basic_1/fsubst0/defs.ma".
 
-theorem fsubst0_ind:
+implied lemma fsubst0_ind:
  \forall (i: nat).(\forall (v: T).(\forall (c1: C).(\forall (t1: T).(\forall 
 (P: ((C \to (T \to Prop)))).(((\forall (t2: T).((subst0 i v t1 t2) \to (P c1 
 t2)))) \to (((\forall (c2: C).((csubst0 i v c1 c2) \to (P c2 t1)))) \to 
@@ -33,44 +33,25 @@ C).(\lambda (t: T).(\lambda (f2: (fsubst0 i v c1 t1 c t)).(match f2 with
 [(fsubst0_snd x x0) \Rightarrow (f x x0) | (fsubst0_fst x x0) \Rightarrow (f0 
 x x0) | (fsubst0_both x x0 x1 x2) \Rightarrow (f1 x x0 x1 x2)]))))))))))).
 
-theorem fsubst0_gen_base:
+lemma fsubst0_gen_base:
  \forall (c1: C).(\forall (c2: C).(\forall (t1: T).(\forall (t2: T).(\forall 
 (v: T).(\forall (i: nat).((fsubst0 i v c1 t1 c2 t2) \to (or3 (land (eq C c1 
 c2) (subst0 i v t1 t2)) (land (eq T t1 t2) (csubst0 i v c1 c2)) (land (subst0 
 i v t1 t2) (csubst0 i v c1 c2)))))))))
 \def
  \lambda (c1: C).(\lambda (c2: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda 
-(v: T).(\lambda (i: nat).(\lambda (H: (fsubst0 i v c1 t1 c2 t2)).(let TMP_10 
-\def (\lambda (c: C).(\lambda (t: T).(let TMP_1 \def (eq C c1 c) in (let 
-TMP_2 \def (subst0 i v t1 t) in (let TMP_3 \def (land TMP_1 TMP_2) in (let 
-TMP_4 \def (eq T t1 t) in (let TMP_5 \def (csubst0 i v c1 c) in (let TMP_6 
-\def (land TMP_4 TMP_5) in (let TMP_7 \def (subst0 i v t1 t) in (let TMP_8 
-\def (csubst0 i v c1 c) in (let TMP_9 \def (land TMP_7 TMP_8) in (or3 TMP_3 
-TMP_6 TMP_9)))))))))))) in (let TMP_24 \def (\lambda (t0: T).(\lambda (H0: 
-(subst0 i v t1 t0)).(let TMP_11 \def (eq C c1 c1) in (let TMP_12 \def (subst0 
-i v t1 t0) in (let TMP_13 \def (land TMP_11 TMP_12) in (let TMP_14 \def (eq T 
-t1 t0) in (let TMP_15 \def (csubst0 i v c1 c1) in (let TMP_16 \def (land 
-TMP_14 TMP_15) in (let TMP_17 \def (subst0 i v t1 t0) in (let TMP_18 \def 
-(csubst0 i v c1 c1) in (let TMP_19 \def (land TMP_17 TMP_18) in (let TMP_20 
-\def (eq C c1 c1) in (let TMP_21 \def (subst0 i v t1 t0) in (let TMP_22 \def 
-(refl_equal C c1) in (let TMP_23 \def (conj TMP_20 TMP_21 TMP_22 H0) in 
-(or3_intro0 TMP_13 TMP_16 TMP_19 TMP_23)))))))))))))))) in (let TMP_38 \def 
-(\lambda (c0: C).(\lambda (H0: (csubst0 i v c1 c0)).(let TMP_25 \def (eq C c1 
-c0) in (let TMP_26 \def (subst0 i v t1 t1) in (let TMP_27 \def (land TMP_25 
-TMP_26) in (let TMP_28 \def (eq T t1 t1) in (let TMP_29 \def (csubst0 i v c1 
-c0) in (let TMP_30 \def (land TMP_28 TMP_29) in (let TMP_31 \def (subst0 i v 
-t1 t1) in (let TMP_32 \def (csubst0 i v c1 c0) in (let TMP_33 \def (land 
-TMP_31 TMP_32) in (let TMP_34 \def (eq T t1 t1) in (let TMP_35 \def (csubst0 
-i v c1 c0) in (let TMP_36 \def (refl_equal T t1) in (let TMP_37 \def (conj 
-TMP_34 TMP_35 TMP_36 H0) in (or3_intro1 TMP_27 TMP_30 TMP_33 
-TMP_37)))))))))))))))) in (let TMP_51 \def (\lambda (t0: T).(\lambda (H0: 
-(subst0 i v t1 t0)).(\lambda (c0: C).(\lambda (H1: (csubst0 i v c1 c0)).(let 
-TMP_39 \def (eq C c1 c0) in (let TMP_40 \def (subst0 i v t1 t0) in (let 
-TMP_41 \def (land TMP_39 TMP_40) in (let TMP_42 \def (eq T t1 t0) in (let 
-TMP_43 \def (csubst0 i v c1 c0) in (let TMP_44 \def (land TMP_42 TMP_43) in 
-(let TMP_45 \def (subst0 i v t1 t0) in (let TMP_46 \def (csubst0 i v c1 c0) 
-in (let TMP_47 \def (land TMP_45 TMP_46) in (let TMP_48 \def (subst0 i v t1 
-t0) in (let TMP_49 \def (csubst0 i v c1 c0) in (let TMP_50 \def (conj TMP_48 
-TMP_49 H0 H1) in (or3_intro2 TMP_41 TMP_44 TMP_47 TMP_50))))))))))))))))) in 
-(fsubst0_ind i v c1 t1 TMP_10 TMP_24 TMP_38 TMP_51 c2 t2 H))))))))))).
+(v: T).(\lambda (i: nat).(\lambda (H: (fsubst0 i v c1 t1 c2 t2)).(fsubst0_ind 
+i v c1 t1 (\lambda (c: C).(\lambda (t: T).(or3 (land (eq C c1 c) (subst0 i v 
+t1 t)) (land (eq T t1 t) (csubst0 i v c1 c)) (land (subst0 i v t1 t) (csubst0 
+i v c1 c))))) (\lambda (t0: T).(\lambda (H0: (subst0 i v t1 t0)).(or3_intro0 
+(land (eq C c1 c1) (subst0 i v t1 t0)) (land (eq T t1 t0) (csubst0 i v c1 
+c1)) (land (subst0 i v t1 t0) (csubst0 i v c1 c1)) (conj (eq C c1 c1) (subst0 
+i v t1 t0) (refl_equal C c1) H0)))) (\lambda (c0: C).(\lambda (H0: (csubst0 i 
+v c1 c0)).(or3_intro1 (land (eq C c1 c0) (subst0 i v t1 t1)) (land (eq T t1 
+t1) (csubst0 i v c1 c0)) (land (subst0 i v t1 t1) (csubst0 i v c1 c0)) (conj 
+(eq T t1 t1) (csubst0 i v c1 c0) (refl_equal T t1) H0)))) (\lambda (t0: 
+T).(\lambda (H0: (subst0 i v t1 t0)).(\lambda (c0: C).(\lambda (H1: (csubst0 
+i v c1 c0)).(or3_intro2 (land (eq C c1 c0) (subst0 i v t1 t0)) (land (eq T t1 
+t0) (csubst0 i v c1 c0)) (land (subst0 i v t1 t0) (csubst0 i v c1 c0)) (conj 
+(subst0 i v t1 t0) (csubst0 i v c1 c0) H0 H1)))))) c2 t2 H))))))).