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<b>set </b><font color="Maroon" title="c3">f</font> = <font color="Maroon" title="c1">S</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c2">T</font>;<br/>
<b>let </b><font color="Maroon" title="c4">W</font> be    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_3.html#D8" title="WAYBEL_3:def.8">WAYBEL_3:def 8</a><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:14_1_1_1"/>
(  not <font color="Maroon" title="c1">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c1">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_1"><b>suppose </b></a><a NAME="E1:14_1_1_1_1"/><i><font color="Green" title="E9">A1</font></i>: 
not <font color="Maroon" title="c1">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/><div class="add"><b>assume </b><a NAME="E2:14_1_1_1_1"/>
<font color="Maroon" title="c4">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c2">T</font></span>)</span>
 ;<br/><a NAME="E3:14_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">T</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="waybel17.html#E1:14_1_1_1_1"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a></i>;<br/><b>hence </b><a NAME="E4:14_1_1_1_1"/>
<font color="Maroon" title="c4">W</font> is <a href="orders_2.html#V2" title="ORDERS_2:attr.2">reflexive</a>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2"><b>suppose </b></a><a NAME="E1:14_1_1_1_2"/><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c1">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/><div class="add"><b>assume </b><a NAME="E2:14_1_1_1_2"/>
<font color="Maroon" title="c4">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c2">T</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E3:14_1_1_1_2"/>
<font color="Maroon" title="c4">W</font> is <a href="orders_2.html#V2" title="ORDERS_2:attr.2">reflexive</a>
 <b>by </b><i><a class="txt" href="waybel17.html#E1:14_1_1_1_2"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="funcop_1.html#T16" title="FUNCOP_1:th.16">FUNCOP_1:16</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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