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<b>consider </b><font color="Maroon" title="c3">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> <b> such that </b><br/><a NAME="E2:11_2_1"/><i><font color="Green" title="E8">A14</font></i>: 
( <font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> or <font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">k</font> )
 <b>by </b><i><a class="ref" href="int_1.html#T8" target="_self" title="INT_1:th.8">Th8</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">l</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> <b> such that </b><br/><a NAME="E4:11_2_1"/><i><font color="Green" title="E9">A15</font></i>: 
( <font color="Maroon" title="c2">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">l</font> or <font color="Maroon" title="c2">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">l</font> )
 <b>by </b><i><a class="ref" href="int_1.html#T8" target="_self" title="INT_1:th.8">Th8</a></i>;<br/>
<div><i><font color="Green" title="E10">A17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1_1"/>
( <font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c2">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">l</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">i2</font> is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a></span><br/><a NAME="E2:11_2_1_1"/><b>then </b>
<font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c4">l</font>
 ;<br/><b>hence </b><a NAME="E3:11_2_1_1"/>
<font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">i2</font> is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1_2"/>
( ( <font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c2">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">l</font> ) or ( <font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c2">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">l</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">i2</font> is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a></span><br/><a NAME="E2:11_2_1_2"/><b>then </b>
<font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c4">l</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E3:11_2_1_2"/>
<font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">i2</font> is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>
 <b>by </b><i><a class="ref" href="int_1.html#T7" target="_self" title="INT_1:th.7">Th7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:11_2_1"/>
<font color="Maroon" title="c1">i1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">i2</font> is <a href="int_1.html#V1" title="INT_1:attr.1">integer</a>
 <b>by </b><i><a class="txt" href="#E2:11_2_1"><i><font color="Green" title="E8">A14</font></i></a>, <a class="txt" href="#E4:11_2_1"><i><font color="Green" title="E9">A15</font></i></a>, <a class="txt" href="#E5:11_2_1"><i><font color="Green" title="E10">A17</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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