X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Ftlist%2Fprops.ma;fp=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Ftlist%2Fprops.ma;h=0000000000000000000000000000000000000000;hb=88a68a9c334646bc17314d5327cd3b790202acd6;hp=92b0d05ffa1b186877b57effe12c71ee93e47deb;hpb=4904accd80118cb8126e308ae098d87f8651c9f4;p=helm.git diff --git a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/tlist/props.ma b/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/tlist/props.ma deleted file mode 100644 index 92b0d05ff..000000000 --- a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/tlist/props.ma +++ /dev/null @@ -1,131 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||M|| *) -(* ||A|| A project by Andrea Asperti *) -(* ||T|| *) -(* ||I|| Developers: *) -(* ||T|| The HELM team. *) -(* ||A|| http://helm.cs.unibo.it *) -(* \ / *) -(* \ / This file is distributed under the terms of the *) -(* v GNU General Public License Version 2 *) -(* *) -(**************************************************************************) - -(* This file was automatically generated: do not edit *********************) - -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: - \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 - \lambda (k: K).(\lambda (v: T).(\lambda (t: T).(\lambda (vs: -TList).(TList_ind (\lambda (t0: TList).(eq T (THeads k (TApp t0 v) t) (THeads -k t0 (THead k v t)))) (refl_equal T (THead k v t)) (\lambda (t0: T).(\lambda -(t1: TList).(\lambda (H: (eq T (THeads k (TApp t1 v) t) (THeads k t1 (THead k -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: - \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)))))) -\def - \lambda (ts1: TList).(TList_ind (\lambda (t: TList).(\forall (t1: T).(ex2_2 -TList T (\lambda (ts2: TList).(\lambda (t2: T).(eq TList (TCons t1 t) (TApp -ts2 t2)))) (\lambda (ts2: TList).(\lambda (_: T).(eq nat (tslen t) (tslen -ts2))))))) (\lambda (t1: T).(ex2_2_intro TList T (\lambda (ts2: -TList).(\lambda (t2: T).(eq TList (TCons t1 TNil) (TApp ts2 t2)))) (\lambda -(ts2: TList).(\lambda (_: T).(eq nat O (tslen ts2)))) TNil t1 (refl_equal -TList (TApp TNil t1)) (refl_equal nat (tslen TNil)))) (\lambda (t: -T).(\lambda (t0: TList).(\lambda (H: ((\forall (t1: T).(ex2_2 TList T -(\lambda (ts2: TList).(\lambda (t2: T).(eq TList (TCons t1 t0) (TApp ts2 -t2)))) (\lambda (ts2: TList).(\lambda (_: T).(eq nat (tslen t0) (tslen -ts2)))))))).(\lambda (t1: T).(let H_x \def (H t) in (let H0 \def H_x in -(ex2_2_ind TList T (\lambda (ts2: TList).(\lambda (t2: T).(eq TList (TCons t -t0) (TApp ts2 t2)))) (\lambda (ts2: TList).(\lambda (_: T).(eq nat (tslen t0) -(tslen ts2)))) (ex2_2 TList T (\lambda (ts2: TList).(\lambda (t2: T).(eq -TList (TCons t1 (TCons t t0)) (TApp ts2 t2)))) (\lambda (ts2: TList).(\lambda -(_: T).(eq nat (S (tslen t0)) (tslen ts2))))) (\lambda (x0: TList).(\lambda -(x1: T).(\lambda (H1: (eq TList (TCons t t0) (TApp x0 x1))).(\lambda (H2: (eq -nat (tslen t0) (tslen x0))).(eq_ind_r TList (TApp x0 x1) (\lambda (t2: -TList).(ex2_2 TList T (\lambda (ts2: TList).(\lambda (t3: T).(eq TList (TCons -t1 t2) (TApp ts2 t3)))) (\lambda (ts2: TList).(\lambda (_: T).(eq nat (S -(tslen t0)) (tslen ts2)))))) (eq_ind_r nat (tslen x0) (\lambda (n: -nat).(ex2_2 TList T (\lambda (ts2: TList).(\lambda (t2: T).(eq TList (TCons -t1 (TApp x0 x1)) (TApp ts2 t2)))) (\lambda (ts2: TList).(\lambda (_: T).(eq -nat (S n) (tslen ts2)))))) (ex2_2_intro TList T (\lambda (ts2: -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 *) -