X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fflt%2Fprops.ma;fp=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fflt%2Fprops.ma;h=0000000000000000000000000000000000000000;hb=88a68a9c334646bc17314d5327cd3b790202acd6;hp=57df415280d93642d7112713353370bc504c4475;hpb=4904accd80118cb8126e308ae098d87f8651c9f4;p=helm.git diff --git a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/flt/props.ma b/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/flt/props.ma deleted file mode 100644 index 57df41528..000000000 --- a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/flt/props.ma +++ /dev/null @@ -1,154 +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/flt/defs.ma". - -include "Basic-1/C/props.ma". - -theorem flt_thead_sx: - \forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt c u c -(THead k u t))))) -\def - \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t: -T).(le_lt_plus_plus (cweight c) (cweight c) (tweight u) (S (plus (tweight u) -(tweight t))) (le_n (cweight c)) (le_n_S (tweight u) (plus (tweight u) -(tweight t)) (le_plus_l (tweight u) (tweight t))))))). -(* COMMENTS -Initial nodes: 65 -END *) - -theorem flt_thead_dx: - \forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt c t c -(THead k u t))))) -\def - \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t: -T).(le_lt_plus_plus (cweight c) (cweight c) (tweight t) (S (plus (tweight u) -(tweight t))) (le_n (cweight c)) (le_n_S (tweight t) (plus (tweight u) -(tweight t)) (le_plus_r (tweight u) (tweight t))))))). -(* COMMENTS -Initial nodes: 65 -END *) - -theorem flt_shift: - \forall (k: K).(\forall (c: C).(\forall (u: T).(\forall (t: T).(flt (CHead c -k u) t c (THead k u t))))) -\def - \lambda (_: K).(\lambda (c: C).(\lambda (u: T).(\lambda (t: T).(eq_ind nat -(S (plus (cweight c) (plus (tweight u) (tweight t)))) (\lambda (n: nat).(lt -(plus (plus (cweight c) (tweight u)) (tweight t)) n)) (eq_ind_r nat (plus -(plus (cweight c) (tweight u)) (tweight t)) (\lambda (n: nat).(lt (plus (plus -(cweight c) (tweight u)) (tweight t)) (S n))) (le_n (S (plus (plus (cweight -c) (tweight u)) (tweight t)))) (plus (cweight c) (plus (tweight u) (tweight -t))) (plus_assoc_l (cweight c) (tweight u) (tweight t))) (plus (cweight c) (S -(plus (tweight u) (tweight t)))) (plus_n_Sm (cweight c) (plus (tweight u) -(tweight t))))))). -(* COMMENTS -Initial nodes: 179 -END *) - -theorem flt_arith0: - \forall (k: K).(\forall (c: C).(\forall (t: T).(\forall (i: nat).(flt c t -(CHead c k t) (TLRef i))))) -\def - \lambda (_: K).(\lambda (c: C).(\lambda (t: T).(\lambda (_: -nat).(lt_x_plus_x_Sy (plus (cweight c) (tweight t)) O)))). -(* COMMENTS -Initial nodes: 21 -END *) - -theorem flt_arith1: - \forall (k1: K).(\forall (c1: C).(\forall (c2: C).(\forall (t1: T).((cle -(CHead c1 k1 t1) c2) \to (\forall (k2: K).(\forall (t2: T).(\forall (i: -nat).(flt c1 t1 (CHead c2 k2 t2) (TLRef i))))))))) -\def - \lambda (_: K).(\lambda (c1: C).(\lambda (c2: C).(\lambda (t1: T).(\lambda -(H: (le (plus (cweight c1) (tweight t1)) (cweight c2))).(\lambda (_: -K).(\lambda (t2: T).(\lambda (_: nat).(le_lt_trans (plus (cweight c1) -(tweight t1)) (cweight c2) (plus (plus (cweight c2) (tweight t2)) (S O)) H -(eq_ind_r nat (plus (S O) (plus (cweight c2) (tweight t2))) (\lambda (n: -nat).(lt (cweight c2) n)) (le_lt_n_Sm (cweight c2) (plus (cweight c2) -(tweight t2)) (le_plus_l (cweight c2) (tweight t2))) (plus (plus (cweight c2) -(tweight t2)) (S O)) (plus_sym (plus (cweight c2) (tweight t2)) (S -O))))))))))). -(* COMMENTS -Initial nodes: 151 -END *) - -theorem flt_arith2: - \forall (c1: C).(\forall (c2: C).(\forall (t1: T).(\forall (i: nat).((flt c1 -t1 c2 (TLRef i)) \to (\forall (k2: K).(\forall (t2: T).(\forall (j: nat).(flt -c1 t1 (CHead c2 k2 t2) (TLRef j))))))))) -\def - \lambda (c1: C).(\lambda (c2: C).(\lambda (t1: T).(\lambda (_: nat).(\lambda -(H: (lt (plus (cweight c1) (tweight t1)) (plus (cweight c2) (S O)))).(\lambda -(_: K).(\lambda (t2: T).(\lambda (_: nat).(lt_le_trans (plus (cweight c1) -(tweight t1)) (plus (cweight c2) (S O)) (plus (plus (cweight c2) (tweight -t2)) (S O)) H (le_plus_plus (cweight c2) (plus (cweight c2) (tweight t2)) (S -O) (S O) (le_plus_l (cweight c2) (tweight t2)) (le_n (S O))))))))))). -(* COMMENTS -Initial nodes: 115 -END *) - -theorem flt_trans: - \forall (c1: C).(\forall (c2: C).(\forall (t1: T).(\forall (t2: T).((flt c1 -t1 c2 t2) \to (\forall (c3: C).(\forall (t3: T).((flt c2 t2 c3 t3) \to (flt -c1 t1 c3 t3)))))))) -\def - \lambda (c1: C).(\lambda (c2: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda -(H: (lt (fweight c1 t1) (fweight c2 t2))).(\lambda (c3: C).(\lambda (t3: -T).(\lambda (H0: (lt (fweight c2 t2) (fweight c3 t3))).(lt_trans (fweight c1 -t1) (fweight c2 t2) (fweight c3 t3) H H0)))))))). -(* COMMENTS -Initial nodes: 63 -END *) - -theorem flt_wf__q_ind: - \forall (P: ((C \to (T \to Prop)))).(((\forall (n: nat).((\lambda (P0: ((C -\to (T \to Prop)))).(\lambda (n0: nat).(\forall (c: C).(\forall (t: T).((eq -nat (fweight c t) n0) \to (P0 c t)))))) P n))) \to (\forall (c: C).(\forall -(t: T).(P c t)))) -\def - let Q \def (\lambda (P: ((C \to (T \to Prop)))).(\lambda (n: nat).(\forall -(c: C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t)))))) in (\lambda -(P: ((C \to (T \to Prop)))).(\lambda (H: ((\forall (n: nat).(\forall (c: -C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t))))))).(\lambda (c: -C).(\lambda (t: T).(H (fweight c t) c t (refl_equal nat (fweight c t))))))). -(* COMMENTS -Initial nodes: 85 -END *) - -theorem flt_wf_ind: - \forall (P: ((C \to (T \to Prop)))).(((\forall (c2: C).(\forall (t2: -T).(((\forall (c1: C).(\forall (t1: T).((flt c1 t1 c2 t2) \to (P c1 t1))))) -\to (P c2 t2))))) \to (\forall (c: C).(\forall (t: T).(P c t)))) -\def - let Q \def (\lambda (P: ((C \to (T \to Prop)))).(\lambda (n: nat).(\forall -(c: C).(\forall (t: T).((eq nat (fweight c t) n) \to (P c t)))))) in (\lambda -(P: ((C \to (T \to Prop)))).(\lambda (H: ((\forall (c2: C).(\forall (t2: -T).(((\forall (c1: C).(\forall (t1: T).((flt c1 t1 c2 t2) \to (P c1 t1))))) -\to (P c2 t2)))))).(\lambda (c: C).(\lambda (t: T).(flt_wf__q_ind P (\lambda -(n: nat).(lt_wf_ind n (Q P) (\lambda (n0: nat).(\lambda (H0: ((\forall (m: -nat).((lt m n0) \to (Q P m))))).(\lambda (c0: C).(\lambda (t0: T).(\lambda -(H1: (eq nat (fweight c0 t0) n0)).(let H2 \def (eq_ind_r nat n0 (\lambda (n1: -nat).(\forall (m: nat).((lt m n1) \to (\forall (c1: C).(\forall (t1: T).((eq -nat (fweight c1 t1) m) \to (P c1 t1))))))) H0 (fweight c0 t0) H1) in (H c0 t0 -(\lambda (c1: C).(\lambda (t1: T).(\lambda (H3: (flt c1 t1 c0 t0)).(H2 -(fweight c1 t1) H3 c1 t1 (refl_equal nat (fweight c1 t1))))))))))))))) c -t))))). -(* COMMENTS -Initial nodes: 211 -END *) -