eq over SET1 and SET no longer used

[helm.git] / helm / software / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / fsubst0 / fwd.ma

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/fsubst0/fwd.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/fsubst0/fwd.ma
index 7df3bf8bba641860451d31aa56da7851b94db514..bdf51216e3ab2c88a7964b80bcbad9733497b1ef 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/fsubst0/fwd.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/fsubst0/fwd.ma
@@ -23,43 +23,18 @@ 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 H0 \def 
-(match H in fsubst0 return (\lambda (c: C).(\lambda (t: T).(\lambda (_: 
-(fsubst0 ? ? ? ? c t)).((eq C c c2) \to ((eq T t 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)))))))) with [(fsubst0_snd t0 H0) \Rightarrow 
-(\lambda (H1: (eq C c1 c2)).(\lambda (H2: (eq T t0 t2)).(eq_ind C c2 (\lambda 
-(c: C).((eq T t0 t2) \to ((subst0 i v t1 t0) \to (or3 (land (eq C c c2) 
-(subst0 i v t1 t2)) (land (eq T t1 t2) (csubst0 i v c c2)) (land (subst0 i v 
-t1 t2) (csubst0 i v c c2)))))) (\lambda (H3: (eq T t0 t2)).(eq_ind T t2 
-(\lambda (t: T).((subst0 i v t1 t) \to (or3 (land (eq C c2 c2) (subst0 i v t1 
-t2)) (land (eq T t1 t2) (csubst0 i v c2 c2)) (land (subst0 i v t1 t2) 
-(csubst0 i v c2 c2))))) (\lambda (H4: (subst0 i v t1 t2)).(or3_intro0 (land 
-(eq C c2 c2) (subst0 i v t1 t2)) (land (eq T t1 t2) (csubst0 i v c2 c2)) 
-(land (subst0 i v t1 t2) (csubst0 i v c2 c2)) (conj (eq C c2 c2) (subst0 i v 
-t1 t2) (refl_equal C c2) H4))) t0 (sym_eq T t0 t2 H3))) c1 (sym_eq C c1 c2 
-H1) H2 H0))) | (fsubst0_fst c0 H0) \Rightarrow (\lambda (H1: (eq C c0 
-c2)).(\lambda (H2: (eq T t1 t2)).(eq_ind C c2 (\lambda (c: C).((eq T t1 t2) 
-\to ((csubst0 i v c1 c) \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)))))) (\lambda (H3: (eq T t1 t2)).(eq_ind T t2 (\lambda (t: T).((csubst0 i 
-v c1 c2) \to (or3 (land (eq C c1 c2) (subst0 i v t t2)) (land (eq T t t2) 
-(csubst0 i v c1 c2)) (land (subst0 i v t t2) (csubst0 i v c1 c2))))) (\lambda 
-(H4: (csubst0 i v c1 c2)).(or3_intro1 (land (eq C c1 c2) (subst0 i v t2 t2)) 
-(land (eq T t2 t2) (csubst0 i v c1 c2)) (land (subst0 i v t2 t2) (csubst0 i v 
-c1 c2)) (conj (eq T t2 t2) (csubst0 i v c1 c2) (refl_equal T t2) H4))) t1 
-(sym_eq T t1 t2 H3))) c0 (sym_eq C c0 c2 H1) H2 H0))) | (fsubst0_both t0 H0 
-c0 H1) \Rightarrow (\lambda (H2: (eq C c0 c2)).(\lambda (H3: (eq T t0 
-t2)).(eq_ind C c2 (\lambda (c: C).((eq T t0 t2) \to ((subst0 i v t1 t0) \to 
-((csubst0 i v c1 c) \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))))))) (\lambda (H4: (eq T t0 t2)).(eq_ind T t2 (\lambda (t: T).((subst0 i 
-v t1 t) \to ((csubst0 i v c1 c2) \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)))))) (\lambda (H5: (subst0 i v t1 t2)).(\lambda (H6: 
-(csubst0 i v c1 c2)).(or3_intro2 (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)) (conj (subst0 i v t1 t2) (csubst0 i v c1 c2) H5 H6)))) t0 (sym_eq T t0 
-t2 H4))) c0 (sym_eq C c0 c2 H2) H3 H0 H1)))]) in (H0 (refl_equal C c2) 
-(refl_equal T t2))))))))).
+(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))))))).