(* This file was automatically generated: do not edit *********************)
-include "Basic-1/T/defs.ma".
+include "basic_1/T/fwd.ma".
theorem not_abbr_abst:
not (eq B Abbr Abst)
\def
- \lambda (H: (eq B Abbr Abst)).(let H0 \def (eq_ind B Abbr (\lambda (ee:
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow True |
-Abst \Rightarrow False | Void \Rightarrow False])) I Abst H) in (False_ind
-False H0)).
-(* COMMENTS
-Initial nodes: 34
-END *)
+ \lambda (H: (eq B Abbr Abst)).(let TMP_1 \def (\lambda (ee: B).(match ee in
+B with [Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow
+False])) in (let H0 \def (eq_ind B Abbr TMP_1 I Abst H) in (False_ind False
+H0))).
theorem not_void_abst:
not (eq B Void Abst)
\def
- \lambda (H: (eq B Void Abst)).(let H0 \def (eq_ind B Void (\lambda (ee:
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow False |
-Abst \Rightarrow False | Void \Rightarrow True])) I Abst H) in (False_ind
-False H0)).
-(* COMMENTS
-Initial nodes: 34
-END *)
+ \lambda (H: (eq B Void Abst)).(let TMP_2 \def (\lambda (ee: B).(match ee in
+B with [Abbr \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow
+True])) in (let H0 \def (eq_ind B Void TMP_2 I Abst H) in (False_ind False
+H0))).
theorem not_abbr_void:
not (eq B Abbr Void)
\def
- \lambda (H: (eq B Abbr Void)).(let H0 \def (eq_ind B Abbr (\lambda (ee:
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow True |
-Abst \Rightarrow False | Void \Rightarrow False])) I Void H) in (False_ind
-False H0)).
-(* COMMENTS
-Initial nodes: 34
-END *)
+ \lambda (H: (eq B Abbr Void)).(let TMP_3 \def (\lambda (ee: B).(match ee in
+B with [Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow
+False])) in (let H0 \def (eq_ind B Abbr TMP_3 I Void H) in (False_ind False
+H0))).
theorem not_abst_void:
not (eq B Abst Void)
\def
- \lambda (H: (eq B Abst Void)).(let H0 \def (eq_ind B Abst (\lambda (ee:
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow False |
-Abst \Rightarrow True | Void \Rightarrow False])) I Void H) in (False_ind
-False H0)).
-(* COMMENTS
-Initial nodes: 34
-END *)
-
-theorem thead_x_y_y:
- \forall (k: K).(\forall (v: T).(\forall (t: T).((eq T (THead k v t) t) \to
-(\forall (P: Prop).P))))
-\def
- \lambda (k: K).(\lambda (v: T).(\lambda (t: T).(T_ind (\lambda (t0: T).((eq
-T (THead k v t0) t0) \to (\forall (P: Prop).P))) (\lambda (n: nat).(\lambda
-(H: (eq T (THead k v (TSort n)) (TSort n))).(\lambda (P: Prop).(let H0 \def
-(eq_ind T (THead k v (TSort n)) (\lambda (ee: T).(match ee in T return
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TSort n) H) in
-(False_ind P H0))))) (\lambda (n: nat).(\lambda (H: (eq T (THead k v (TLRef
-n)) (TLRef n))).(\lambda (P: Prop).(let H0 \def (eq_ind T (THead k v (TLRef
-n)) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort
-_) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _)
-\Rightarrow True])) I (TLRef n) H) in (False_ind P H0))))) (\lambda (k0:
-K).(\lambda (t0: T).(\lambda (_: (((eq T (THead k v t0) t0) \to (\forall (P:
-Prop).P)))).(\lambda (t1: T).(\lambda (H0: (((eq T (THead k v t1) t1) \to
-(\forall (P: Prop).P)))).(\lambda (H1: (eq T (THead k v (THead k0 t0 t1))
-(THead k0 t0 t1))).(\lambda (P: Prop).(let H2 \def (f_equal T K (\lambda (e:
-T).(match e in T return (\lambda (_: T).K) with [(TSort _) \Rightarrow k |
-(TLRef _) \Rightarrow k | (THead k1 _ _) \Rightarrow k1])) (THead k v (THead
-k0 t0 t1)) (THead k0 t0 t1) H1) in ((let H3 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow v |
-(TLRef _) \Rightarrow v | (THead _ t2 _) \Rightarrow t2])) (THead k v (THead
-k0 t0 t1)) (THead k0 t0 t1) H1) in ((let H4 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow (THead
-k0 t0 t1) | (TLRef _) \Rightarrow (THead k0 t0 t1) | (THead _ _ t2)
-\Rightarrow t2])) (THead k v (THead k0 t0 t1)) (THead k0 t0 t1) H1) in
-(\lambda (H5: (eq T v t0)).(\lambda (H6: (eq K k k0)).(let H7 \def (eq_ind T
-v (\lambda (t2: T).((eq T (THead k t2 t1) t1) \to (\forall (P0: Prop).P0)))
-H0 t0 H5) in (let H8 \def (eq_ind K k (\lambda (k1: K).((eq T (THead k1 t0
-t1) t1) \to (\forall (P0: Prop).P0))) H7 k0 H6) in (H8 H4 P)))))) H3))
-H2))))))))) t))).
-(* COMMENTS
-Initial nodes: 461
-END *)
+ \lambda (H: (eq B Abst Void)).(let TMP_4 \def (\lambda (ee: B).(match ee in
+B with [Abbr \Rightarrow False | Abst \Rightarrow True | Void \Rightarrow
+False])) in (let H0 \def (eq_ind B Abst TMP_4 I Void H) in (False_ind False
+H0))).
theorem tweight_lt:
\forall (t: T).(lt O (tweight t))
\def
- \lambda (t: T).(T_ind (\lambda (t0: T).(lt O (tweight t0))) (\lambda (_:
-nat).(le_n (S O))) (\lambda (_: nat).(le_n (S O))) (\lambda (_: K).(\lambda
-(t0: T).(\lambda (H: (lt O (tweight t0))).(\lambda (t1: T).(\lambda (_: (lt O
-(tweight t1))).(le_S (S O) (plus (tweight t0) (tweight t1)) (le_plus_trans (S
-O) (tweight t0) (tweight t1) H))))))) t).
-(* COMMENTS
-Initial nodes: 85
-END *)
+ \lambda (t: T).(let TMP_1848 \def (\lambda (t0: T).(let TMP_1847 \def
+(tweight t0) in (lt O TMP_1847))) in (let TMP_1846 \def (\lambda (_:
+nat).(let TMP_1845 \def (S O) in (le_n TMP_1845))) in (let TMP_1844 \def
+(\lambda (_: nat).(let TMP_1843 \def (S O) in (le_n TMP_1843))) in (let
+TMP_1842 \def (\lambda (_: K).(\lambda (t0: T).(\lambda (H: (lt O (tweight
+t0))).(\lambda (t1: T).(\lambda (_: (lt O (tweight t1))).(let TMP_1841 \def
+(S O) in (let TMP_1839 \def (tweight t0) in (let TMP_1838 \def (tweight t1)
+in (let TMP_1840 \def (plus TMP_1839 TMP_1838) in (let TMP_1836 \def (S O) in
+(let TMP_1835 \def (tweight t0) in (let TMP_1834 \def (tweight t1) in (let
+TMP_1837 \def (le_plus_trans TMP_1836 TMP_1835 TMP_1834 H) in (le_S TMP_1841
+TMP_1840 TMP_1837)))))))))))))) in (T_ind TMP_1848 TMP_1846 TMP_1844 TMP_1842
+t))))).
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