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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is <a href="membered.html#V6" title="MEMBERED:attr.6">natural-membered</a> implies <font color="Maroon" title="c1">X</font> is <a href="membered.html#V5" title="MEMBERED:attr.5">integer-membered</a> )</span><br/>

<b>assume </b><a NAME="E1:2_1_1"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c1">X</font> is <a href="membered.html#V6" title="MEMBERED:attr.6">natural-membered</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">X</font> is <a href="membered.html#V5" title="MEMBERED:attr.5">integer-membered</a></span><br/>

<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="membered.html#D5" target="_self" title="MEMBERED:def.5">MEMBERED:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c2">x</font> is <a href="int_1.html#V1" title="INT_1:attr.1">integer</a> )</span><br/>

<b>assume </b><a NAME="E2:2_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> is <a href="int_1.html#V1" title="INT_1:attr.1">integer</a></span><br/>

<a NAME="E3:2_1_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>
 
<b>by </b><i><a class="txt" href="#E1:2_1_1"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="membered.html#D6" target="_self" title="MEMBERED:def.6">Def6</a></i>;<br/>
<a NAME="E4:2_1_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E5:2_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="ref" href="numbers.html#T17" title="NUMBERS:th.17">NUMBERS:17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</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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