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

<span class="kw">let </span><font color="Maroon" title="c1">j1</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</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">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gr_cy_1.html#K5" title="GR_CY_1:func.5">@'</a> 1</span>)</span> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> <font color="Maroon" title="c1">j1</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E2:31"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
( <font color="Maroon" title="c1">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font> or <font color="Maroon" title="c1">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> <font color="Maroon" title="c2">k</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T2" title="INT_1:th.2">INT_1:2</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:31_1"/>
( <font color="Maroon" title="c1">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font> or <font color="Maroon" title="c1">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> <font color="Maroon" title="c2">k</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31"><span class="lab"><font color="Green" title="E20">A1</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1"><span class="kw">suppose </span></a><a NAME="E1:31_1_1"/>
<font color="Maroon" title="c1">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font>
 ; <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">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gr_cy_1.html#K5" title="GR_CY_1:func.5">@'</a> 1</span>)</span> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> <font color="Maroon" title="c1">j1</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:31_1_1"/>
<font color="Maroon" title="c1">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gr_cy_1.html#K5" title="GR_CY_1:func.5">@'</a> 1</span>)</span> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> <font color="Maroon" title="c1">j1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="gr_cy_1.html#E25"><span class="lab"><font color="Green" title="E18">Lm4</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_2"><span class="kw">suppose </span></a><a NAME="E1:31_1_2"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<font color="Maroon" title="c1">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> <font color="Maroon" title="c2">k</font>
 ; <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">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gr_cy_1.html#K5" title="GR_CY_1:func.5">@'</a> 1</span>)</span> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> <font color="Maroon" title="c1">j1</font></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c3">k9</font> = <font color="Maroon" title="c2">k</font> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c4">k9</font> = <font color="Maroon" title="c3">k9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="gr_cy_1.html#K2" title="GR_CY_1:func.2">INT.Group</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></span>;<br/><span class="p1">(<span class="default"><a href="gr_cy_1.html#K5" title="GR_CY_1:func.5">@'</a> 1</span>)</span> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> <font color="Maroon" title="c1">j1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K5" title="GR_CY_1:func.5">@'</a> 1</span>)</span> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_2"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="group_1.html#T36" title="GROUP_1:th.36">GROUP_1:36</a></span>
<br/>.= 
<font color="Maroon" title="c4">k9</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="gr_cy_1.html#E25"><span class="lab"><font color="Green" title="E18">Lm4</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c1">j1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1_2"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="gr_cy_1.html#T15" target="_self" title="GR_CY_1:th.15">Th37</a></span>
;<br/><span class="kw">hence </span><a NAME="E5:31_1_2"/>
<font color="Maroon" title="c1">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gr_cy_1.html#K5" title="GR_CY_1:func.5">@'</a> 1</span>)</span> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> <font color="Maroon" title="c1">j1</font>
 ; <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></div><span class="kw">end;</span></div>

</div>
