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<b>let </b><font color="Maroon" title="c1">r</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">r</font> is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> implies ( <font color="Maroon" title="c1">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> &amp; <font color="Maroon" title="c1">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ) )</span><br/>

<b>assume </b><a NAME="E1:17"/>
<font color="Maroon" title="c1">r</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"> ( <font color="Maroon" title="c1">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> &amp; <font color="Maroon" title="c1">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> )</span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">i1</font> = <font color="Maroon" title="c1">r</font> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/>
<a NAME="E3:17"/>
( <font color="Maroon" title="c2">i1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> &amp; <font color="Maroon" title="c2">i1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> )
 
;<br/>
<b>hence </b><a NAME="E4:17"/>
( <font color="Maroon" title="c1">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 is   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> &amp; <font color="Maroon" title="c1">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 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/>


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