<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">w1</font>, <font color="Maroon" title="c2">w2</font> be   <a href="supinf_1.html#NM1" title="SUPINF_1:NM.1">R_eal</a>; <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">  for <font color="Olive" title="b1">wr1</font>, <font color="Olive" title="b2">wr2</font>, <font color="Olive" title="b3">p1</font>, <font color="Olive" title="b4">p2</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Maroon" title="c1">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">wr1</font> &amp; <font color="Maroon" title="c2">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">wr2</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">p1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">wr1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">p2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b2">wr2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">p1</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c1">w1</font></span>)</span> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">p2</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c2">w2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">wr1</font>, <font color="Maroon" title="c4">wr2</font>, <font color="Maroon" title="c5">p1</font>, <font color="Maroon" title="c6">p2</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>; <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="c1">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">wr1</font> &amp; <font color="Maroon" title="c2">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">wr2</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c5">p1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">wr1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">wr2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p1</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c1">w1</font></span>)</span> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p2</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c2">w2</font></span>)</span> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
<font color="Maroon" title="c1">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">wr1</font>
 <span class="kw">and </span><br/><a NAME="E2:26"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<font color="Maroon" title="c2">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">wr2</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">wr1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">wr2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p1</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c1">w1</font></span>)</span> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p2</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c2">w2</font></span>)</span></span><br/>

<a NAME="E3:26"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
<font color="Maroon" title="c6">p2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">wr2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">p2</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c2">w2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="extreal1.html#T1" onmouseover="rs('extreal1/T1')" onmouseout="rh()">EXTREAL1:1</a></span>;<br/>
<a NAME="E4:26"/>
<font color="Maroon" title="c5">p1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">wr1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c1">w1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="extreal1.html#T1" onmouseover="rs('extreal1/T1')" onmouseout="rh()">EXTREAL1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:26"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">p1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">wr1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">wr2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p1</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c1">w1</font></span>)</span> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p2</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c2">w2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="supinf_2.html#T1" onmouseover="rs('supinf_2/T1')" onmouseout="rh()">SUPINF_2:1</a></span>; <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/>


</div>
