X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fprocedural%2FCoq%2FArith%2FDiv2.mma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fprocedural%2FCoq%2FArith%2FDiv2.mma;h=48ace138d7070e00144a0ec6561327adafe02a4d;hb=29714797b01e0ac8c22e4df2827b1785a759f482;hp=0000000000000000000000000000000000000000;hpb=1fb0f39de8b87920d2f15f9e33929d372fa518dd;p=helm.git diff --git a/helm/software/matita/contribs/procedural/Coq/Arith/Div2.mma b/helm/software/matita/contribs/procedural/Coq/Arith/Div2.mma new file mode 100644 index 000000000..48ace138d --- /dev/null +++ b/helm/software/matita/contribs/procedural/Coq/Arith/Div2.mma @@ -0,0 +1,127 @@ +(**************************************************************************) +(* ___ *) +(* ||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 "Coq.ma". + +(*#**********************************************************************) + +(* v * The Coq Proof Assistant / The Coq Development Team *) + +(* n/2 < n] *) + +inline procedural "cic:/Coq/Arith/Div2/lt_div2.con" as lemma. + +(* UNEXPORTED +Hint Resolve lt_div2: arith. +*) + +(*#* Properties related to the parity *) + +inline procedural "cic:/Coq/Arith/Div2/even_odd_div2.con" as lemma. + +(*#* Specializations *) + +inline procedural "cic:/Coq/Arith/Div2/even_div2.con" as lemma. + +inline procedural "cic:/Coq/Arith/Div2/div2_even.con" as lemma. + +inline procedural "cic:/Coq/Arith/Div2/odd_div2.con" as lemma. + +inline procedural "cic:/Coq/Arith/Div2/div2_odd.con" as lemma. + +(* UNEXPORTED +Hint Resolve even_div2 div2_even odd_div2 div2_odd: arith. +*) + +(*#* Properties related to the double ([2n]) *) + +inline procedural "cic:/Coq/Arith/Div2/double.con" as definition. + +(* UNEXPORTED +Hint Unfold double: arith. +*) + +inline procedural "cic:/Coq/Arith/Div2/double_S.con" as lemma. + +inline procedural "cic:/Coq/Arith/Div2/double_plus.con" as lemma. + +(* UNEXPORTED +Hint Resolve double_S: arith. +*) + +inline procedural "cic:/Coq/Arith/Div2/even_odd_double.con" as lemma. + +(*#* Specializations *) + +inline procedural "cic:/Coq/Arith/Div2/even_double.con" as lemma. + +inline procedural "cic:/Coq/Arith/Div2/double_even.con" as lemma. + +inline procedural "cic:/Coq/Arith/Div2/odd_double.con" as lemma. + +inline procedural "cic:/Coq/Arith/Div2/double_odd.con" as lemma. + +(* UNEXPORTED +Hint Resolve even_double double_even odd_double double_odd: arith. +*) + +(*#* Application: + - if [n] is even then there is a [p] such that [n = 2p] + - if [n] is odd then there is a [p] such that [n = 2p+1] + + (Immediate: it is [n/2]) *) + +inline procedural "cic:/Coq/Arith/Div2/even_2n.con" as lemma. + +inline procedural "cic:/Coq/Arith/Div2/odd_S2n.con" as lemma. +