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<span class="kw">let </span><font color="Maroon" title="c1">a</font> be   <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">b</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   holds <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b1">b</font> is  <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">b</font> be   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">b</font> is  <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a> </span><br/>



<a NAME="E1:50"/>
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">b</font> is  <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_5.html#T39" target="_self" title="BORSUK_5:th.39">Th39</a></span>;<br/>
<a NAME="E2:50"/><span class="kw">then </span>
<font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">b</font></span>)</span> is  <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_5.html#T38" target="_self" title="BORSUK_5:th.38">Th38</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:50"/>
<font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">b</font> is  <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</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/>


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