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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be   <a href="supinf_1.html#NM1" title="SUPINF_1:NM.1">R_eal</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">a</font>, <font color="Olive" title="b2">b</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> holds <br/><font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <font color="Olive" title="b2">b</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</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">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> implies <font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <font color="Maroon" title="c4">b</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:34"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ; <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">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <font color="Maroon" title="c4">b</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c6">b</font> = <font color="Maroon" title="c4">b</font> as   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">c</font> being   <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <span class="kw"> such that </span><br/><a NAME="E4:34"/><span class="lab"><font color="Green" title="E4">W1</font></span>: 
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c</font>
 <span class="kw">and </span><br/><a NAME="E5:34"/><span class="lab"><font color="Green" title="E5">W2</font></span>: 
<font color="Maroon" title="c2">y</font> <a href="xxreal_3.html#K5" title="XXREAL_3:func.5">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="xxreal_3.html#D6" title="XXREAL_3:def.6">XXREAL_3:def 6</a></span>;<br/>
<font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <font color="Maroon" title="c2">y</font> = 
<font color="Maroon" title="c1">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="xxreal_3.html#K5" title="XXREAL_3:func.5">"</a> </span>)</span>

<br/>.= 
<font color="Maroon" title="c5">a</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">c</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="txt" href="#E5:34"><span class="lab"><font color="Green" title="E5">W2</font></span></a>, <a class="ref" href="xxreal_3.html#D5" title="XXREAL_3:def.5">XXREAL_3:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c5">a</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <font color="Maroon" title="c6">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:34"><span class="lab"><font color="Green" title="E5">W2</font></span></a>, <a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="txt" href="#E4:34"><span class="lab"><font color="Green" title="E4">W1</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E7:34"/>
<font color="Maroon" title="c1">x</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <font color="Maroon" title="c4">b</font>
 ; <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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