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<b>consider </b><font color="Maroon" title="c4">s1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">S</font>;<br/>
<b>consider </b><font color="Maroon" title="c5">t1</font>, <font color="Maroon" title="c6">t2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">T</font><b> such that </b><br/><a NAME="E3:3_1_1"/><i><font color="Green" title="E1">A1</font></i>: 
<font color="Maroon" title="c5">t1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">t2</font>
 <b>by </b><i><a class="ref" href="yellow_8.html#D1" title="YELLOW_8:def.1">YELLOW_8:def 1</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:3_1_1_1"/>
( <font color="Maroon" title="c4">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">t1</font> or <font color="Maroon" title="c4">s1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">t1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1"><b>suppose </b></a><a NAME="E1:3_1_1_1_1"/>
<font color="Maroon" title="c4">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">t1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="brouwer.html#K1" title="BROUWER:func.1">DiffElems</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a></span><br/><div class="add"><a NAME="E2:3_1_1_1_1"/><b>then </b>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c6">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="brouwer.html#K1" title="BROUWER:func.1">DiffElems</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font>
 <b>by </b><i><a class="txt" href="brouwer.html#E3:3_1_1"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:3_1_1_1_1"/>
not  <a href="brouwer.html#K1" title="BROUWER:func.1">DiffElems</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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="hsNdiv(this)" href="javascript:()" title="3_1_1_1_2"><b>suppose </b></a><a NAME="E1:3_1_1_1_2"/>
<font color="Maroon" title="c4">s1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">t1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="brouwer.html#K1" title="BROUWER:func.1">DiffElems</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a></span><br/><div class="add"><a NAME="E2:3_1_1_1_2"/><b>then </b>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c5">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="brouwer.html#K1" title="BROUWER:func.1">DiffElems</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font>
 ;<br/><b>hence </b><a NAME="E3:3_1_1_1_2"/>
not  <a href="brouwer.html#K1" title="BROUWER:func.1">DiffElems</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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><b>end;</b></div>

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