(\lambda (n1: nat).(\lambda (n2: nat).(\lambda (t3: T).(\lambda (H0: (iso
(TSort n2) t3)).(let H1 \def (match H0 in iso return (\lambda (t: T).(\lambda
(t0: T).(\lambda (_: (iso t t0)).((eq T t (TSort n2)) \to ((eq T t0 t3) \to
-(iso (TSort n1) t3)))))) with [(iso_sort n0 n3) \Rightarrow (\lambda (H0: (eq
-T (TSort n0) (TSort n2))).(\lambda (H1: (eq T (TSort n3) t3)).((let H2 \def
+(iso (TSort n1) t3)))))) with [(iso_sort n0 n3) \Rightarrow (\lambda (H1: (eq
+T (TSort n0) (TSort n2))).(\lambda (H2: (eq T (TSort n3) t3)).((let H3 \def
(f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with
[(TSort n) \Rightarrow n | (TLRef _) \Rightarrow n0 | (THead _ _ _)
-\Rightarrow n0])) (TSort n0) (TSort n2) H0) in (eq_ind nat n2 (\lambda (_:
-nat).((eq T (TSort n3) t3) \to (iso (TSort n1) t3))) (\lambda (H3: (eq T
+\Rightarrow n0])) (TSort n0) (TSort n2) H1) in (eq_ind nat n2 (\lambda (_:
+nat).((eq T (TSort n3) t3) \to (iso (TSort n1) t3))) (\lambda (H4: (eq T
(TSort n3) t3)).(eq_ind T (TSort n3) (\lambda (t: T).(iso (TSort n1) t))
-(iso_sort n1 n3) t3 H3)) n0 (sym_eq nat n0 n2 H2))) H1))) | (iso_lref i1 i2)
-\Rightarrow (\lambda (H0: (eq T (TLRef i1) (TSort n2))).(\lambda (H1: (eq T
-(TLRef i2) t3)).((let H2 \def (eq_ind T (TLRef i1) (\lambda (e: T).(match e
+(iso_sort n1 n3) t3 H4)) n0 (sym_eq nat n0 n2 H3))) H2))) | (iso_lref i1 i2)
+\Rightarrow (\lambda (H1: (eq T (TLRef i1) (TSort n2))).(\lambda (H2: (eq T
+(TLRef i2) t3)).((let H3 \def (eq_ind T (TLRef i1) (\lambda (e: T).(match e
in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef
-_) \Rightarrow True | (THead _ _ _) \Rightarrow False])) I (TSort n2) H0) in
-(False_ind ((eq T (TLRef i2) t3) \to (iso (TSort n1) t3)) H2)) H1))) |
-(iso_head k v1 v2 t1 t2) \Rightarrow (\lambda (H0: (eq T (THead k v1 t1)
-(TSort n2))).(\lambda (H1: (eq T (THead k v2 t2) t3)).((let H2 \def (eq_ind T
-(THead k v1 t1) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop)
+_) \Rightarrow True | (THead _ _ _) \Rightarrow False])) I (TSort n2) H1) in
+(False_ind ((eq T (TLRef i2) t3) \to (iso (TSort n1) t3)) H3)) H2))) |
+(iso_head k v1 v2 t0 t4) \Rightarrow (\lambda (H1: (eq T (THead k v1 t0)
+(TSort n2))).(\lambda (H2: (eq T (THead k v2 t4) t3)).((let H3 \def (eq_ind T
+(THead k v1 t0) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop)
with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _
-_) \Rightarrow True])) I (TSort n2) H0) in (False_ind ((eq T (THead k v2 t2)
-t3) \to (iso (TSort n1) t3)) H2)) H1)))]) in (H1 (refl_equal T (TSort n2))
+_) \Rightarrow True])) I (TSort n2) H1) in (False_ind ((eq T (THead k v2 t4)
+t3) \to (iso (TSort n1) t3)) H3)) H2)))]) in (H1 (refl_equal T (TSort n2))
(refl_equal T t3))))))) (\lambda (i1: nat).(\lambda (i2: nat).(\lambda (t3:
T).(\lambda (H0: (iso (TLRef i2) t3)).(let H1 \def (match H0 in iso return
(\lambda (t: T).(\lambda (t0: T).(\lambda (_: (iso t t0)).((eq T t (TLRef
i2)) \to ((eq T t0 t3) \to (iso (TLRef i1) t3)))))) with [(iso_sort n1 n2)
-\Rightarrow (\lambda (H0: (eq T (TSort n1) (TLRef i2))).(\lambda (H1: (eq T
-(TSort n2) t3)).((let H2 \def (eq_ind T (TSort n1) (\lambda (e: T).(match e
+\Rightarrow (\lambda (H1: (eq T (TSort n1) (TLRef i2))).(\lambda (H2: (eq T
+(TSort n2) t3)).((let H3 \def (eq_ind T (TSort n1) (\lambda (e: T).(match e
in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow True | (TLRef
-_) \Rightarrow False | (THead _ _ _) \Rightarrow False])) I (TLRef i2) H0) in
-(False_ind ((eq T (TSort n2) t3) \to (iso (TLRef i1) t3)) H2)) H1))) |
-(iso_lref i0 i3) \Rightarrow (\lambda (H0: (eq T (TLRef i0) (TLRef
-i2))).(\lambda (H1: (eq T (TLRef i3) t3)).((let H2 \def (f_equal T nat
+_) \Rightarrow False | (THead _ _ _) \Rightarrow False])) I (TLRef i2) H1) in
+(False_ind ((eq T (TSort n2) t3) \to (iso (TLRef i1) t3)) H3)) H2))) |
+(iso_lref i0 i3) \Rightarrow (\lambda (H1: (eq T (TLRef i0) (TLRef
+i2))).(\lambda (H2: (eq T (TLRef i3) t3)).((let H3 \def (f_equal T nat
(\lambda (e: T).(match e in T return (\lambda (_: T).nat) with [(TSort _)
\Rightarrow i0 | (TLRef n) \Rightarrow n | (THead _ _ _) \Rightarrow i0]))
-(TLRef i0) (TLRef i2) H0) in (eq_ind nat i2 (\lambda (_: nat).((eq T (TLRef
-i3) t3) \to (iso (TLRef i1) t3))) (\lambda (H3: (eq T (TLRef i3) t3)).(eq_ind
-T (TLRef i3) (\lambda (t: T).(iso (TLRef i1) t)) (iso_lref i1 i3) t3 H3)) i0
-(sym_eq nat i0 i2 H2))) H1))) | (iso_head k v1 v2 t1 t2) \Rightarrow (\lambda
-(H0: (eq T (THead k v1 t1) (TLRef i2))).(\lambda (H1: (eq T (THead k v2 t2)
-t3)).((let H2 \def (eq_ind T (THead k v1 t1) (\lambda (e: T).(match e in T
+(TLRef i0) (TLRef i2) H1) in (eq_ind nat i2 (\lambda (_: nat).((eq T (TLRef
+i3) t3) \to (iso (TLRef i1) t3))) (\lambda (H4: (eq T (TLRef i3) t3)).(eq_ind
+T (TLRef i3) (\lambda (t: T).(iso (TLRef i1) t)) (iso_lref i1 i3) t3 H4)) i0
+(sym_eq nat i0 i2 H3))) H2))) | (iso_head k v1 v2 t0 t4) \Rightarrow (\lambda
+(H1: (eq T (THead k v1 t0) (TLRef i2))).(\lambda (H2: (eq T (THead k v2 t4)
+t3)).((let H3 \def (eq_ind T (THead k v1 t0) (\lambda (e: T).(match e in T
return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TLRef i2) H0) in
-(False_ind ((eq T (THead k v2 t2) t3) \to (iso (TLRef i1) t3)) H2)) H1)))])
+\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TLRef i2) H1) in
+(False_ind ((eq T (THead k v2 t4) t3) \to (iso (TLRef i1) t3)) H3)) H2)))])
in (H1 (refl_equal T (TLRef i2)) (refl_equal T t3))))))) (\lambda (k:
K).(\lambda (v1: T).(\lambda (v2: T).(\lambda (t3: T).(\lambda (t4:
T).(\lambda (t5: T).(\lambda (H0: (iso (THead k v2 t4) t5)).(let H1 \def
(match H0 in iso return (\lambda (t: T).(\lambda (t0: T).(\lambda (_: (iso t
t0)).((eq T t (THead k v2 t4)) \to ((eq T t0 t5) \to (iso (THead k v1 t3)
-t5)))))) with [(iso_sort n1 n2) \Rightarrow (\lambda (H0: (eq T (TSort n1)
-(THead k v2 t4))).(\lambda (H1: (eq T (TSort n2) t5)).((let H2 \def (eq_ind T
+t5)))))) with [(iso_sort n1 n2) \Rightarrow (\lambda (H1: (eq T (TSort n1)
+(THead k v2 t4))).(\lambda (H2: (eq T (TSort n2) t5)).((let H3 \def (eq_ind T
(TSort n1) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with
[(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _)
-\Rightarrow False])) I (THead k v2 t4) H0) in (False_ind ((eq T (TSort n2)
-t5) \to (iso (THead k v1 t3) t5)) H2)) H1))) | (iso_lref i1 i2) \Rightarrow
-(\lambda (H0: (eq T (TLRef i1) (THead k v2 t4))).(\lambda (H1: (eq T (TLRef
-i2) t5)).((let H2 \def (eq_ind T (TLRef i1) (\lambda (e: T).(match e in T
+\Rightarrow False])) I (THead k v2 t4) H1) in (False_ind ((eq T (TSort n2)
+t5) \to (iso (THead k v1 t3) t5)) H3)) H2))) | (iso_lref i1 i2) \Rightarrow
+(\lambda (H1: (eq T (TLRef i1) (THead k v2 t4))).(\lambda (H2: (eq T (TLRef
+i2) t5)).((let H3 \def (eq_ind T (TLRef i1) (\lambda (e: T).(match e in T
return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead k v2 t4) H0)
-in (False_ind ((eq T (TLRef i2) t5) \to (iso (THead k v1 t3) t5)) H2)) H1)))
-| (iso_head k0 v0 v3 t0 t4) \Rightarrow (\lambda (H0: (eq T (THead k0 v0 t0)
-(THead k v2 t4))).(\lambda (H1: (eq T (THead k0 v3 t4) t5)).((let H2 \def
+\Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead k v2 t4) H1)
+in (False_ind ((eq T (TLRef i2) t5) \to (iso (THead k v1 t3) t5)) H3)) H2)))
+| (iso_head k0 v0 v3 t0 t6) \Rightarrow (\lambda (H1: (eq T (THead k0 v0 t0)
+(THead k v2 t4))).(\lambda (H2: (eq T (THead k0 v3 t6) t5)).((let H3 \def
(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
[(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t)
-\Rightarrow t])) (THead k0 v0 t0) (THead k v2 t4) H0) in ((let H3 \def
+\Rightarrow t])) (THead k0 v0 t0) (THead k v2 t4) H1) in ((let H4 \def
(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
[(TSort _) \Rightarrow v0 | (TLRef _) \Rightarrow v0 | (THead _ t _)
-\Rightarrow t])) (THead k0 v0 t0) (THead k v2 t4) H0) in ((let H4 \def
+\Rightarrow t])) (THead k0 v0 t0) (THead k v2 t4) H1) in ((let H5 \def
(f_equal T K (\lambda (e: T).(match e in T return (\lambda (_: T).K) with
-[(TSort _) \Rightarrow k0 | (TLRef _) \Rightarrow k0 | (THead k _ _)
-\Rightarrow k])) (THead k0 v0 t0) (THead k v2 t4) H0) in (eq_ind K k (\lambda
-(k1: K).((eq T v0 v2) \to ((eq T t0 t4) \to ((eq T (THead k1 v3 t4) t5) \to
-(iso (THead k v1 t3) t5))))) (\lambda (H5: (eq T v0 v2)).(eq_ind T v2
-(\lambda (_: T).((eq T t0 t4) \to ((eq T (THead k v3 t4) t5) \to (iso (THead
-k v1 t3) t5)))) (\lambda (H6: (eq T t0 t4)).(eq_ind T t4 (\lambda (_: T).((eq
-T (THead k v3 t4) t5) \to (iso (THead k v1 t3) t5))) (\lambda (H7: (eq T
-(THead k v3 t4) t5)).(eq_ind T (THead k v3 t4) (\lambda (t: T).(iso (THead k
-v1 t3) t)) (iso_head k v1 v3 t3 t4) t5 H7)) t0 (sym_eq T t0 t4 H6))) v0
-(sym_eq T v0 v2 H5))) k0 (sym_eq K k0 k H4))) H3)) H2)) H1)))]) in (H1
+[(TSort _) \Rightarrow k0 | (TLRef _) \Rightarrow k0 | (THead k1 _ _)
+\Rightarrow k1])) (THead k0 v0 t0) (THead k v2 t4) H1) in (eq_ind K k
+(\lambda (k1: K).((eq T v0 v2) \to ((eq T t0 t4) \to ((eq T (THead k1 v3 t6)
+t5) \to (iso (THead k v1 t3) t5))))) (\lambda (H6: (eq T v0 v2)).(eq_ind T v2
+(\lambda (_: T).((eq T t0 t4) \to ((eq T (THead k v3 t6) t5) \to (iso (THead
+k v1 t3) t5)))) (\lambda (H7: (eq T t0 t4)).(eq_ind T t4 (\lambda (_: T).((eq
+T (THead k v3 t6) t5) \to (iso (THead k v1 t3) t5))) (\lambda (H8: (eq T
+(THead k v3 t6) t5)).(eq_ind T (THead k v3 t6) (\lambda (t: T).(iso (THead k
+v1 t3) t)) (iso_head k v1 v3 t3 t6) t5 H8)) t0 (sym_eq T t0 t4 H7))) v0
+(sym_eq T v0 v2 H6))) k0 (sym_eq K k0 k H5))) H4)) H3)) H2)))]) in (H1
(refl_equal T (THead k v2 t4)) (refl_equal T t5)))))))))) t1 t2 H))).
projects / helm.git / blobdiff