update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / tlist / props.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/tlist/props.ma b/matita/matita/contribs/lambdadelta/basic_1/tlist/props.ma
index 92b0d05ffa1b186877b57effe12c71ee93e47deb..267f9d9ad45f18554c0b0180e416666294e00bed 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/tlist/props.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/tlist/props.ma
@@ -14,44 +14,9 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/tlist/defs.ma".
+include "basic_1/tlist/defs.ma".
 
-theorem tslt_wf__q_ind:
- \forall (P: ((TList \to Prop))).(((\forall (n: nat).((\lambda (P0: ((TList 
-\to Prop))).(\lambda (n0: nat).(\forall (ts: TList).((eq nat (tslen ts) n0) 
-\to (P0 ts))))) P n))) \to (\forall (ts: TList).(P ts)))
-\def
- let Q \def (\lambda (P: ((TList \to Prop))).(\lambda (n: nat).(\forall (ts: 
-TList).((eq nat (tslen ts) n) \to (P ts))))) in (\lambda (P: ((TList \to 
-Prop))).(\lambda (H: ((\forall (n: nat).(\forall (ts: TList).((eq nat (tslen 
-ts) n) \to (P ts)))))).(\lambda (ts: TList).(H (tslen ts) ts (refl_equal nat 
-(tslen ts)))))).
-(* COMMENTS
-Initial nodes: 61
-END *)
-
-theorem tslt_wf_ind:
- \forall (P: ((TList \to Prop))).(((\forall (ts2: TList).(((\forall (ts1: 
-TList).((tslt ts1 ts2) \to (P ts1)))) \to (P ts2)))) \to (\forall (ts: 
-TList).(P ts)))
-\def
- let Q \def (\lambda (P: ((TList \to Prop))).(\lambda (n: nat).(\forall (ts: 
-TList).((eq nat (tslen ts) n) \to (P ts))))) in (\lambda (P: ((TList \to 
-Prop))).(\lambda (H: ((\forall (ts2: TList).(((\forall (ts1: TList).((lt 
-(tslen ts1) (tslen ts2)) \to (P ts1)))) \to (P ts2))))).(\lambda (ts: 
-TList).(tslt_wf__q_ind (\lambda (t: TList).(P t)) (\lambda (n: 
-nat).(lt_wf_ind n (Q (\lambda (t: TList).(P t))) (\lambda (n0: nat).(\lambda 
-(H0: ((\forall (m: nat).((lt m n0) \to (Q (\lambda (t: TList).(P t)) 
-m))))).(\lambda (ts0: TList).(\lambda (H1: (eq nat (tslen ts0) n0)).(let H2 
-\def (eq_ind_r nat n0 (\lambda (n1: nat).(\forall (m: nat).((lt m n1) \to 
-(\forall (ts1: TList).((eq nat (tslen ts1) m) \to (P ts1)))))) H0 (tslen ts0) 
-H1) in (H ts0 (\lambda (ts1: TList).(\lambda (H3: (lt (tslen ts1) (tslen 
-ts0))).(H2 (tslen ts1) H3 ts1 (refl_equal nat (tslen ts1))))))))))))) ts)))).
-(* COMMENTS
-Initial nodes: 179
-END *)
-
-theorem theads_tapp:
+lemma theads_tapp:
  \forall (k: K).(\forall (v: T).(\forall (t: T).(\forall (vs: TList).(eq T 
 (THeads k (TApp vs v) t) (THeads k vs (THead k v t))))))
 \def
@@ -62,11 +27,8 @@ k t0 (THead k v t)))) (refl_equal T (THead k v t)) (\lambda (t0: T).(\lambda
 v t)))).(eq_ind T (THeads k (TApp t1 v) t) (\lambda (t2: T).(eq T (THead k t0 
 (THeads k (TApp t1 v) t)) (THead k t0 t2))) (refl_equal T (THead k t0 (THeads 
 k (TApp t1 v) t))) (THeads k t1 (THead k v t)) H)))) vs)))).
-(* COMMENTS
-Initial nodes: 175
-END *)
 
-theorem tcons_tapp_ex:
+lemma tcons_tapp_ex:
  \forall (ts1: TList).(\forall (t1: T).(ex2_2 TList T (\lambda (ts2: 
 TList).(\lambda (t2: T).(eq TList (TCons t1 ts1) (TApp ts2 t2)))) (\lambda 
 (ts2: TList).(\lambda (_: T).(eq nat (tslen ts1) (tslen ts2))))))
@@ -99,33 +61,4 @@ TList).(\lambda (t2: T).(eq TList (TCons t1 (TApp x0 x1)) (TApp ts2 t2))))
 (\lambda (ts2: TList).(\lambda (_: T).(eq nat (S (tslen x0)) (tslen ts2)))) 
 (TCons t1 x0) x1 (refl_equal TList (TApp (TCons t1 x0) x1)) (refl_equal nat 
 (tslen (TCons t1 x0)))) (tslen t0) H2) (TCons t t0) H1))))) H0))))))) ts1).
-(* COMMENTS
-Initial nodes: 503
-END *)
-
-theorem tlist_ind_rev:
- \forall (P: ((TList \to Prop))).((P TNil) \to (((\forall (ts: 
-TList).(\forall (t: T).((P ts) \to (P (TApp ts t)))))) \to (\forall (ts: 
-TList).(P ts))))
-\def
- \lambda (P: ((TList \to Prop))).(\lambda (H: (P TNil)).(\lambda (H0: 
-((\forall (ts: TList).(\forall (t: T).((P ts) \to (P (TApp ts 
-t))))))).(\lambda (ts: TList).(tslt_wf_ind (\lambda (t: TList).(P t)) 
-(\lambda (ts2: TList).(TList_ind (\lambda (t: TList).(((\forall (ts1: 
-TList).((tslt ts1 t) \to (P ts1)))) \to (P t))) (\lambda (_: ((\forall (ts1: 
-TList).((tslt ts1 TNil) \to (P ts1))))).H) (\lambda (t: T).(\lambda (t0: 
-TList).(\lambda (_: ((((\forall (ts1: TList).((tslt ts1 t0) \to (P ts1)))) 
-\to (P t0)))).(\lambda (H2: ((\forall (ts1: TList).((tslt ts1 (TCons t t0)) 
-\to (P ts1))))).(let H_x \def (tcons_tapp_ex t0 t) in (let H3 \def H_x in 
-(ex2_2_ind TList T (\lambda (ts3: TList).(\lambda (t2: T).(eq TList (TCons t 
-t0) (TApp ts3 t2)))) (\lambda (ts3: TList).(\lambda (_: T).(eq nat (tslen t0) 
-(tslen ts3)))) (P (TCons t t0)) (\lambda (x0: TList).(\lambda (x1: 
-T).(\lambda (H4: (eq TList (TCons t t0) (TApp x0 x1))).(\lambda (H5: (eq nat 
-(tslen t0) (tslen x0))).(eq_ind_r TList (TApp x0 x1) (\lambda (t1: TList).(P 
-t1)) (H0 x0 x1 (H2 x0 (eq_ind nat (tslen t0) (\lambda (n: nat).(lt n (tslen 
-(TCons t t0)))) (le_n (tslen (TCons t t0))) (tslen x0) H5))) (TCons t t0) 
-H4))))) H3))))))) ts2)) ts)))).
-(* COMMENTS
-Initial nodes: 273
-END *)