X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fsubst%2Ffwd.ma;fp=matitaB%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fsubst%2Ffwd.ma;h=0000000000000000000000000000000000000000;hb=88a68a9c334646bc17314d5327cd3b790202acd6;hp=a0678e5fba7541273d0ad153f15e7a5780544199;hpb=4904accd80118cb8126e308ae098d87f8651c9f4;p=helm.git diff --git a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/subst/fwd.ma b/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/subst/fwd.ma deleted file mode 100644 index a0678e5fb..000000000 --- a/matitaB/matita/contribs/LAMBDA-TYPES/Basic-1/subst/fwd.ma +++ /dev/null @@ -1,79 +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/defs.ma". - -theorem subst_sort: - \forall (v: T).(\forall (d: nat).(\forall (k: nat).(eq T (subst d v (TSort -k)) (TSort k)))) -\def - \lambda (_: T).(\lambda (_: nat).(\lambda (k: nat).(refl_equal T (TSort -k)))). -(* COMMENTS -Initial nodes: 13 -END *) - -theorem subst_lref_lt: - \forall (v: T).(\forall (d: nat).(\forall (i: nat).((lt i d) \to (eq T -(subst d v (TLRef i)) (TLRef i))))) -\def - \lambda (v: T).(\lambda (d: nat).(\lambda (i: nat).(\lambda (H: (lt i -d)).(eq_ind_r bool true (\lambda (b: bool).(eq T (match b with [true -\Rightarrow (TLRef i) | false \Rightarrow (match (blt d i) with [true -\Rightarrow (TLRef (pred i)) | false \Rightarrow (lift d O v)])]) (TLRef i))) -(refl_equal T (TLRef i)) (blt i d) (lt_blt d i H))))). -(* COMMENTS -Initial nodes: 73 -END *) - -theorem subst_lref_eq: - \forall (v: T).(\forall (i: nat).(eq T (subst i v (TLRef i)) (lift i O v))) -\def - \lambda (v: T).(\lambda (i: nat).(eq_ind_r bool false (\lambda (b: bool).(eq -T (match b with [true \Rightarrow (TLRef i) | false \Rightarrow (match b with -[true \Rightarrow (TLRef (pred i)) | false \Rightarrow (lift i O v)])]) (lift -i O v))) (refl_equal T (lift i O v)) (blt i i) (le_bge i i (le_n i)))). -(* COMMENTS -Initial nodes: 71 -END *) - -theorem subst_lref_gt: - \forall (v: T).(\forall (d: nat).(\forall (i: nat).((lt d i) \to (eq T -(subst d v (TLRef i)) (TLRef (pred i)))))) -\def - \lambda (v: T).(\lambda (d: nat).(\lambda (i: nat).(\lambda (H: (lt d -i)).(eq_ind_r bool false (\lambda (b: bool).(eq T (match b with [true -\Rightarrow (TLRef i) | false \Rightarrow (match (blt d i) with [true -\Rightarrow (TLRef (pred i)) | false \Rightarrow (lift d O v)])]) (TLRef -(pred i)))) (eq_ind_r bool true (\lambda (b: bool).(eq T (match b with [true -\Rightarrow (TLRef (pred i)) | false \Rightarrow (lift d O v)]) (TLRef (pred -i)))) (refl_equal T (TLRef (pred i))) (blt d i) (lt_blt i d H)) (blt i d) -(le_bge d i (lt_le_weak d i H)))))). -(* COMMENTS -Initial nodes: 130 -END *) - -theorem subst_head: - \forall (k: K).(\forall (w: T).(\forall (u: T).(\forall (t: T).(\forall (d: -nat).(eq T (subst d w (THead k u t)) (THead k (subst d w u) (subst (s k d) w -t))))))) -\def - \lambda (k: K).(\lambda (w: T).(\lambda (u: T).(\lambda (t: T).(\lambda (d: -nat).(refl_equal T (THead k (subst d w u) (subst (s k d) w t))))))). -(* COMMENTS -Initial nodes: 37 -END *) -