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<span class="kw">consider </span><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/>
<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E3:3_1_1"/><span class="lab"><font color="Green" title="E1">A1</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_8.html#D1" title="YELLOW_8:def.1">YELLOW_8:def 1</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></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"><span class="kw">suppose </span></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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"/><span class="kw">then </span>
<span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[</a><span class="default"><font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c6">t2</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">]</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></a></span>;<br/><span class="kw">hence </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_2"><span class="kw">suppose </span></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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"/><span class="kw">then </span>
<span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[</a><span class="default"><font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c5">t1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">]</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/><span class="kw">hence </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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