<?xml version="1.0"?>
<div class="add">

<a NAME="E1:37"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K8" title="NAT_LAT:func.8">hcflatplus</a> holds <br/><a href="nat_lat.html#K8" title="NAT_LAT:func.8">hcflatplus</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K8" title="NAT_LAT:func.8">hcflatplus</a> implies <a href="nat_lat.html#K8" title="NAT_LAT:func.8">hcflatplus</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:37_1"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K8" title="NAT_LAT:func.8">hcflatplus</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="nat_lat.html#K8" title="NAT_LAT:func.8">hcflatplus</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font></span><br/>

<a NAME="E2:37_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A3</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>,<a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">y1</font>, <font color="Maroon" title="c3">y2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:37_1"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y1</font>,<font color="Maroon" title="c3">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="relat_1.html#D1" title="RELAT_1:def.1">RELAT_1:def 1</a></span>;<br/>
<a NAME="E5:37_1"/>
( <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>  &amp; <font color="Maroon" title="c3">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E4:37_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">n</font> = <font color="Maroon" title="c2">y1</font>, <font color="Maroon" title="c5">k</font> = <font color="Maroon" title="c3">y2</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> ;<br/>
<a NAME="E7:37_1"/><span class="lab"><font color="Green" title="E21">A5</font></span>: 
<a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c4">n</font>,<font color="Maroon" title="c5">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c5">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_lat.html#D1" target="_self" title="NAT_LAT:def.1">Def3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">n</font> = <font color="Maroon" title="c2">y1</font>, <font color="Maroon" title="c7">k</font> = <font color="Maroon" title="c3">y2</font> as   <a href="nat_lat.html#NM2" title="NAT_LAT:NM.2">NatPlus</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E4:37_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<a NAME="E9:37_1"/>
<a href="nat_lat.html#K8" title="NAT_LAT:func.8">hcflatplus</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c7">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c7">k</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:37_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="nat_lat.html#D8" target="_self" title="NAT_LAT:def.8">Def12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:37_1"/>
<a href="nat_lat.html#K8" title="NAT_LAT:func.8">hcflatplus</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:37"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K8" title="NAT_LAT:func.8">hcflatplus</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>,<a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E3:37"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K8" title="NAT_LAT:func.8">hcflatplus</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>,<a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a>, <a class="ref" href="zfmisc_1.html#T96" title="ZFMISC_1:th.96">ZFMISC_1:96</a></span>;<br/>
<a NAME="E4:37"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A6</font></span>: 
 <a href="nat_lat.html#K8" title="NAT_LAT:func.8">hcflatplus</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="funct_1.html#T46" title="FUNCT_1:th.46">FUNCT_1:46</a></span>;<br/>
<a NAME="E5:37"/><span class="lab"><font color="Green" title="E19">A7</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K9" title="NAT_LAT:func.9">lcmlatplus</a> holds <br/><a href="nat_lat.html#K9" title="NAT_LAT:func.9">lcmlatplus</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K9" title="NAT_LAT:func.9">lcmlatplus</a> implies <a href="nat_lat.html#K9" title="NAT_LAT:func.9">lcmlatplus</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:37_2"/><span class="lab"><font color="Green" title="E20">A8</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K9" title="NAT_LAT:func.9">lcmlatplus</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="nat_lat.html#K9" title="NAT_LAT:func.9">lcmlatplus</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font></span><br/>

<a NAME="E2:37_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A9</font></span>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>,<a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">y1</font>, <font color="Maroon" title="c3">y2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:37_2"/><span class="lab"><font color="Green" title="E22">A10</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y1</font>,<font color="Maroon" title="c3">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_2"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="relat_1.html#D1" title="RELAT_1:def.1">RELAT_1:def 1</a></span>;<br/>
<a NAME="E5:37_2"/>
( <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>  &amp; <font color="Maroon" title="c3">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_2"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E4:37_2"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">n</font> = <font color="Maroon" title="c2">y1</font>, <font color="Maroon" title="c5">k</font> = <font color="Maroon" title="c3">y2</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> ;<br/>
<a NAME="E7:37_2"/><span class="lab"><font color="Green" title="E23">A11</font></span>: 
<a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c4">n</font>,<font color="Maroon" title="c5">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="nat_d.html#K5" title="NAT_D:func.5">lcm</a> <font color="Maroon" title="c5">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_lat.html#D2" target="_self" title="NAT_LAT:def.2">Def4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">n</font> = <font color="Maroon" title="c2">y1</font>, <font color="Maroon" title="c7">k</font> = <font color="Maroon" title="c3">y2</font> as   <a href="nat_lat.html#NM2" title="NAT_LAT:NM.2">NatPlus</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_2"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E4:37_2"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>;<br/>
<a NAME="E9:37_2"/>
<a href="nat_lat.html#K9" title="NAT_LAT:func.9">lcmlatplus</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c7">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c7">k</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:37_2"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="ref" href="nat_lat.html#D9" target="_self" title="NAT_LAT:def.9">Def13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:37_2"/>
<a href="nat_lat.html#K9" title="NAT_LAT:func.9">lcmlatplus</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37_2"><span class="lab"><font color="Green" title="E22">A10</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E6:37"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K9" title="NAT_LAT:func.9">lcmlatplus</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>,<a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E7:37"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K9" title="NAT_LAT:func.9">lcmlatplus</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>,<a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a>, <a class="ref" href="zfmisc_1.html#T96" title="ZFMISC_1:th.96">ZFMISC_1:96</a></span>;<br/>
<a NAME="E8:37"/><span class="kw">then </span>
 <a href="nat_lat.html#K9" title="NAT_LAT:func.9">lcmlatplus</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="ref" href="funct_1.html#T46" title="FUNCT_1:th.46">FUNCT_1:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:37"/>
 <a href="nat_lat.html#K10" title="NAT_LAT:func.10">NatPlus_Lattice</a>  is    <a href="nat_lat.html#M2" title="NAT_LAT:mode.2">SubLattice</a> of  <a href="nat_lat.html#K3" title="NAT_LAT:func.3">Nat_Lattice</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="nat_lat.html#D12" target="_self" title="NAT_LAT:def.12">Def16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
