X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1A%2Ftlist%2Ffwd.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1A%2Ftlist%2Ffwd.ma;h=cced52618dbde3c6b14b1223ce51be0bf339aecd;hb=d2545ffd201b1aa49887313791386add78fa8603;hp=0000000000000000000000000000000000000000;hpb=57ae1762497a5f3ea75740e2908e04adb8642cc2;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_1A/tlist/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1A/tlist/fwd.ma new file mode 100644 index 000000000..cced52618 --- /dev/null +++ b/matita/matita/contribs/lambdadelta/basic_1A/tlist/fwd.ma @@ -0,0 +1,70 @@ +(**************************************************************************) +(* ___ *) +(* ||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_1A/tlist/props.ma". + +fact 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)))))). + +lemma 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)))). + +lemma 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)))). +