X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fsubst%2Fprops.ma;fp=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fsubst%2Fprops.ma;h=0000000000000000000000000000000000000000;hb=88a68a9c334646bc17314d5327cd3b790202acd6;hp=3bad044e3198e9cb33d31e6bd5b1c4f489e7cbee;hpb=4904accd80118cb8126e308ae098d87f8651c9f4;p=helm.git diff --git a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/subst/props.ma b/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/subst/props.ma deleted file mode 100644 index 3bad044e3..000000000 --- a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/subst/props.ma +++ /dev/null @@ -1,116 +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/subst/fwd.ma". - -include "Basic-1/subst0/defs.ma". - -include "Basic-1/lift/props.ma". - -theorem subst_lift_SO: - \forall (v: T).(\forall (t: T).(\forall (d: nat).(eq T (subst d v (lift (S -O) d t)) t))) -\def - \lambda (v: T).(\lambda (t: T).(T_ind (\lambda (t0: T).(\forall (d: nat).(eq -T (subst d v (lift (S O) d t0)) t0))) (\lambda (n: nat).(\lambda (d: -nat).(eq_ind_r T (TSort n) (\lambda (t0: T).(eq T (subst d v t0) (TSort n))) -(eq_ind_r T (TSort n) (\lambda (t0: T).(eq T t0 (TSort n))) (refl_equal T -(TSort n)) (subst d v (TSort n)) (subst_sort v d n)) (lift (S O) d (TSort n)) -(lift_sort n (S O) d)))) (\lambda (n: nat).(\lambda (d: nat).(lt_le_e n d (eq -T (subst d v (lift (S O) d (TLRef n))) (TLRef n)) (\lambda (H: (lt n -d)).(eq_ind_r T (TLRef n) (\lambda (t0: T).(eq T (subst d v t0) (TLRef n))) -(eq_ind_r T (TLRef n) (\lambda (t0: T).(eq T t0 (TLRef n))) (refl_equal T -(TLRef n)) (subst d v (TLRef n)) (subst_lref_lt v d n H)) (lift (S O) d -(TLRef n)) (lift_lref_lt n (S O) d H))) (\lambda (H: (le d n)).(eq_ind_r T -(TLRef (plus n (S O))) (\lambda (t0: T).(eq T (subst d v t0) (TLRef n))) -(eq_ind nat (S (plus n O)) (\lambda (n0: nat).(eq T (subst d v (TLRef n0)) -(TLRef n))) (eq_ind_r T (TLRef (pred (S (plus n O)))) (\lambda (t0: T).(eq T -t0 (TLRef n))) (eq_ind nat (plus n O) (\lambda (n0: nat).(eq T (TLRef n0) -(TLRef n))) (f_equal nat T TLRef (plus n O) n (sym_eq nat n (plus n O) -(plus_n_O n))) (pred (S (plus n O))) (pred_Sn (plus n O))) (subst d v (TLRef -(S (plus n O)))) (subst_lref_gt v d (S (plus n O)) (le_n_S d (plus n O) -(le_plus_trans d n O H)))) (plus n (S O)) (plus_n_Sm n O)) (lift (S O) d -(TLRef n)) (lift_lref_ge n (S O) d H)))))) (\lambda (k: K).(\lambda (t0: -T).(\lambda (H: ((\forall (d: nat).(eq T (subst d v (lift (S O) d t0)) -t0)))).(\lambda (t1: T).(\lambda (H0: ((\forall (d: nat).(eq T (subst d v -(lift (S O) d t1)) t1)))).(\lambda (d: nat).(eq_ind_r T (THead k (lift (S O) -d t0) (lift (S O) (s k d) t1)) (\lambda (t2: T).(eq T (subst d v t2) (THead k -t0 t1))) (eq_ind_r T (THead k (subst d v (lift (S O) d t0)) (subst (s k d) v -(lift (S O) (s k d) t1))) (\lambda (t2: T).(eq T t2 (THead k t0 t1))) -(f_equal3 K T T T THead k k (subst d v (lift (S O) d t0)) t0 (subst (s k d) v -(lift (S O) (s k d) t1)) t1 (refl_equal K k) (H d) (H0 (s k d))) (subst d v -(THead k (lift (S O) d t0) (lift (S O) (s k d) t1))) (subst_head k v (lift (S -O) d t0) (lift (S O) (s k d) t1) d)) (lift (S O) d (THead k t0 t1)) -(lift_head k t0 t1 (S O) d)))))))) t)). -(* COMMENTS -Initial nodes: 879 -END *) - -theorem subst_subst0: - \forall (v: T).(\forall (t1: T).(\forall (t2: T).(\forall (d: nat).((subst0 -d v t1 t2) \to (eq T (subst d v t1) (subst d v t2)))))) -\def - \lambda (v: T).(\lambda (t1: T).(\lambda (t2: T).(\lambda (d: nat).(\lambda -(H: (subst0 d v t1 t2)).(subst0_ind (\lambda (n: nat).(\lambda (t: -T).(\lambda (t0: T).(\lambda (t3: T).(eq T (subst n t t0) (subst n t t3)))))) -(\lambda (v0: T).(\lambda (i: nat).(eq_ind_r T (lift i O v0) (\lambda (t: -T).(eq T t (subst i v0 (lift (S i) O v0)))) (eq_ind nat (plus (S O) i) -(\lambda (n: nat).(eq T (lift i O v0) (subst i v0 (lift n O v0)))) (eq_ind T -(lift (S O) i (lift i O v0)) (\lambda (t: T).(eq T (lift i O v0) (subst i v0 -t))) (eq_ind_r T (lift i O v0) (\lambda (t: T).(eq T (lift i O v0) t)) -(refl_equal T (lift i O v0)) (subst i v0 (lift (S O) i (lift i O v0))) -(subst_lift_SO v0 (lift i O v0) i)) (lift (plus (S O) i) O v0) (lift_free v0 -i (S O) O i (le_n (plus O i)) (le_O_n i))) (S i) (refl_equal nat (S i))) -(subst i v0 (TLRef i)) (subst_lref_eq v0 i)))) (\lambda (v0: T).(\lambda (u2: -T).(\lambda (u1: T).(\lambda (i: nat).(\lambda (_: (subst0 i v0 u1 -u2)).(\lambda (H1: (eq T (subst i v0 u1) (subst i v0 u2))).(\lambda (t: -T).(\lambda (k: K).(eq_ind_r T (THead k (subst i v0 u1) (subst (s k i) v0 t)) -(\lambda (t0: T).(eq T t0 (subst i v0 (THead k u2 t)))) (eq_ind_r T (THead k -(subst i v0 u2) (subst (s k i) v0 t)) (\lambda (t0: T).(eq T (THead k (subst -i v0 u1) (subst (s k i) v0 t)) t0)) (eq_ind_r T (subst i v0 u2) (\lambda (t0: -T).(eq T (THead k t0 (subst (s k i) v0 t)) (THead k (subst i v0 u2) (subst (s -k i) v0 t)))) (refl_equal T (THead k (subst i v0 u2) (subst (s k i) v0 t))) -(subst i v0 u1) H1) (subst i v0 (THead k u2 t)) (subst_head k v0 u2 t i)) -(subst i v0 (THead k u1 t)) (subst_head k v0 u1 t i)))))))))) (\lambda (k: -K).(\lambda (v0: T).(\lambda (t3: T).(\lambda (t4: T).(\lambda (i: -nat).(\lambda (_: (subst0 (s k i) v0 t4 t3)).(\lambda (H1: (eq T (subst (s k -i) v0 t4) (subst (s k i) v0 t3))).(\lambda (u: T).(eq_ind_r T (THead k (subst -i v0 u) (subst (s k i) v0 t4)) (\lambda (t: T).(eq T t (subst i v0 (THead k u -t3)))) (eq_ind_r T (THead k (subst i v0 u) (subst (s k i) v0 t3)) (\lambda -(t: T).(eq T (THead k (subst i v0 u) (subst (s k i) v0 t4)) t)) (eq_ind_r T -(subst (s k i) v0 t3) (\lambda (t: T).(eq T (THead k (subst i v0 u) t) (THead -k (subst i v0 u) (subst (s k i) v0 t3)))) (refl_equal T (THead k (subst i v0 -u) (subst (s k i) v0 t3))) (subst (s k i) v0 t4) H1) (subst i v0 (THead k u -t3)) (subst_head k v0 u t3 i)) (subst i v0 (THead k u t4)) (subst_head k v0 u -t4 i)))))))))) (\lambda (v0: T).(\lambda (u1: T).(\lambda (u2: T).(\lambda -(i: nat).(\lambda (_: (subst0 i v0 u1 u2)).(\lambda (H1: (eq T (subst i v0 -u1) (subst i v0 u2))).(\lambda (k: K).(\lambda (t3: T).(\lambda (t4: -T).(\lambda (_: (subst0 (s k i) v0 t3 t4)).(\lambda (H3: (eq T (subst (s k i) -v0 t3) (subst (s k i) v0 t4))).(eq_ind_r T (THead k (subst i v0 u1) (subst (s -k i) v0 t3)) (\lambda (t: T).(eq T t (subst i v0 (THead k u2 t4)))) (eq_ind_r -T (THead k (subst i v0 u2) (subst (s k i) v0 t4)) (\lambda (t: T).(eq T -(THead k (subst i v0 u1) (subst (s k i) v0 t3)) t)) (eq_ind_r T (subst i v0 -u2) (\lambda (t: T).(eq T (THead k t (subst (s k i) v0 t3)) (THead k (subst i -v0 u2) (subst (s k i) v0 t4)))) (eq_ind_r T (subst (s k i) v0 t4) (\lambda -(t: T).(eq T (THead k (subst i v0 u2) t) (THead k (subst i v0 u2) (subst (s k -i) v0 t4)))) (refl_equal T (THead k (subst i v0 u2) (subst (s k i) v0 t4))) -(subst (s k i) v0 t3) H3) (subst i v0 u1) H1) (subst i v0 (THead k u2 t4)) -(subst_head k v0 u2 t4 i)) (subst i v0 (THead k u1 t3)) (subst_head k v0 u1 -t3 i))))))))))))) d v t1 t2 H))))). -(* COMMENTS -Initial nodes: 1363 -END *) -