X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Fwf_ind%2Fwf2_ind_nlt.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Fwf_ind%2Fwf2_ind_nlt.ma;h=0000000000000000000000000000000000000000;hb=888840f6b3a71d3d686b53b702d362ab90ab0038;hp=492c84cdbfc254fecb632751790d0f413556cc06;hpb=19b0a814861157ba05f23877d5cd94059f52c2e8;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/ground/wf_ind/wf2_ind_nlt.ma b/matita/matita/contribs/lambdadelta/ground/wf_ind/wf2_ind_nlt.ma deleted file mode 100644 index 492c84cdb..000000000 --- a/matita/matita/contribs/lambdadelta/ground/wf_ind/wf2_ind_nlt.ma +++ /dev/null @@ -1,30 +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 *) -(* *) -(**************************************************************************) - -include "ground/arith/nat_lt.ma". - -(* WELL-FOUNDED INDUCTION ***************************************************) - -fact wf2_ind_nlt_aux (A1) (A2) (f:A1→A2→nat) (Q:relation2 …): - (∀n. (∀a1,a2. f a1 a2 < n → Q a1 a2) → ∀a1,a2. f a1 a2 = n → Q a1 a2) → - ∀n,a1,a2. f a1 a2 = n → Q a1 a2. -#A1 #A2 #f #Q #H #n @(nat_ind_lt … n) -n /3 width=3 by/ -qed-. - -(*** f2_ind *) -lemma wf2_ind_nlt (A1) (A2) (f:A1→A2→nat) (Q:relation2 …): - (∀n. (∀a1,a2. f a1 a2 < n → Q a1 a2) → ∀a1,a2. f a1 a2 = n → Q a1 a2) → - ∀a1,a2. Q a1 a2. -#A1 #A2 #f #Q #H #a1 #a2 @(wf2_ind_nlt_aux … H) -H // -qed-.