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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">z</font> be   <a href="xxreal_0.html#NM1" title="XXREAL_0:NM.1">ExtReal</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">x</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  implies <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#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c3">z</font></span>)</span> )</span><br/>





<span class="kw">assume </span><a NAME="E1:158"/>
<font color="Maroon" title="c1">x</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.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">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#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c3">z</font></span>)</span></span><br/>

<span class="kw">then </span><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#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c3">z</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c2">y</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="c1">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <span class="p2">(<span class="default"><a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T95" target="_self" onmouseover="rs('xxreal_3/T95')" onmouseout="rh()">Th95</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> <span class="p1">(<span class="default"><a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T92" target="_self" onmouseover="rs('xxreal_3/T92')" onmouseout="rh()">Th92</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:158"/>
<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#K3" title="XXREAL_3:func.3">-</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="xxreal_3.html#K3" title="XXREAL_3:func.3">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <font color="Maroon" title="c3">z</font></span>)</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/>


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