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<span class="kw">thus </span><a NAME="E1:91_1_1"/>
( <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R4" title="ROUGHS_1:pred.4">_=</a> <font color="Maroon" title="c3">Y</font> implies ( <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c2">X</font> ) )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c2">X</font> implies <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R4" title="ROUGHS_1:pred.4">_=</a> <font color="Maroon" title="c3">Y</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:91_1_1"/>
( <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c2">X</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R4" title="ROUGHS_1:pred.4">_=</a> <font color="Maroon" title="c3">Y</font></span><br/>

<a NAME="E3:91_1_1"/><span class="kw">then </span>
(  <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c3">Y</font> &amp;  <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c2">X</font> )
 
;<br/>
<a NAME="E4:91_1_1"/><span class="kw">then </span>
 <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c3">Y</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E5:91_1_1"/>
<font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R4" title="ROUGHS_1:pred.4">_=</a> <font color="Maroon" title="c3">Y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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