(* This file was automatically generated: do not edit *********************)
-include "Basic-1/T/defs.ma".
+include "basic_1/T/fwd.ma".
-theorem not_abbr_abst:
+lemma 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 *)
+B).(match ee with [Abbr \Rightarrow True | Abst \Rightarrow False | Void
+\Rightarrow False])) I Abst H) in (False_ind False H0)).
-theorem not_void_abst:
+lemma 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 *)
+B).(match ee with [Abbr \Rightarrow False | Abst \Rightarrow False | Void
+\Rightarrow True])) I Abst H) in (False_ind False H0)).
-theorem not_abbr_void:
+lemma 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 *)
+B).(match ee with [Abbr \Rightarrow True | Abst \Rightarrow False | Void
+\Rightarrow False])) I Void H) in (False_ind False H0)).
-theorem not_abst_void:
+lemma 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 *)
+B).(match ee with [Abbr \Rightarrow False | Abst \Rightarrow True | Void
+\Rightarrow False])) I Void H) in (False_ind False H0)).
-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 *)
-
-theorem tweight_lt:
+lemma tweight_lt:
\forall (t: T).(lt O (tweight t))
\def
\lambda (t: T).(T_ind (\lambda (t0: T).(lt O (tweight t0))) (\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 *)
+
+lemma tle_r:
+ \forall (t: T).(tle t t)
+\def
+ \lambda (t: T).(T_ind (\lambda (t0: T).(le (tweight t0) (tweight t0)))
+(\lambda (_: nat).(le_n (S O))) (\lambda (_: nat).(le_n (S O))) (\lambda (_:
+K).(\lambda (t0: T).(\lambda (_: (le (tweight t0) (tweight t0))).(\lambda
+(t1: T).(\lambda (_: (le (tweight t1) (tweight t1))).(le_n (S (plus (tweight
+t0) (tweight t1))))))))) t).