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<span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c5">z</font> be   <a href="gaussint.html#NM1" title="GAUSSINT:NM.1">G_INTEG</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="c3">x</font> <a href="gaussint.html#R2" title="GAUSSINT:pred.2">is_associated_to</a> <font color="Maroon" title="c4">y</font> &amp; <font color="Maroon" title="c4">y</font> <a href="gaussint.html#R2" title="GAUSSINT:pred.2">is_associated_to</a> <font color="Maroon" title="c5">z</font> implies <font color="Maroon" title="c3">x</font> <a href="gaussint.html#R2" title="GAUSSINT:pred.2">is_associated_to</a> <font color="Maroon" title="c5">z</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:106"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
( <font color="Maroon" title="c3">x</font> <a href="gaussint.html#R2" title="GAUSSINT:pred.2">is_associated_to</a> <font color="Maroon" title="c4">y</font> &amp; <font color="Maroon" title="c4">y</font> <a href="gaussint.html#R2" title="GAUSSINT:pred.2">is_associated_to</a> <font color="Maroon" title="c5">z</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="c3">x</font> <a href="gaussint.html#R2" title="GAUSSINT:pred.2">is_associated_to</a> <font color="Maroon" title="c5">z</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c6">c</font> being   <a href="gaussint.html#NM1" title="GAUSSINT:NM.1">G_INTEG</a><span class="kw"> such that </span><br/><a NAME="E3:106"/><span class="lab"><font color="Green" title="E47">A2</font></span>: 
( <font color="Maroon" title="c6">c</font> is  <a href="gaussint.html#V3" title="GAUSSINT:attr.3">g_int_unit</a>  &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="gaussint.html#T40" target="_self" onmouseover="rs('gaussint/T40')" onmouseout="rh()">Th40</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">d</font> being   <a href="gaussint.html#NM1" title="GAUSSINT:NM.1">G_INTEG</a><span class="kw"> such that </span><br/><a NAME="E5:106"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
( <font color="Maroon" title="c7">d</font> is  <a href="gaussint.html#V3" title="GAUSSINT:attr.3">g_int_unit</a>  &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c5">z</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="gaussint.html#T40" target="_self" onmouseover="rs('gaussint/T40')" onmouseout="rh()">Th40</a></span>;<br/>
<a NAME="E6:106"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c7">d</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c5">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:106"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="txt" href="#E5:106"><span class="lab"><font color="Green" title="E48">A3</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">e</font> = <font color="Maroon" title="c6">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c7">d</font> as   <a href="gaussint.html#NM1" title="GAUSSINT:NM.1">G_INTEG</a> ;<br/>
 <a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c8">e</font> = 
1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c7">d</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:106"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="gaussint.html#T34" target="_self" onmouseover="rs('gaussint/T34')" onmouseout="rh()">Th34</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:106"><span class="lab"><font color="Green" title="E48">A3</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E9:106"/>
<font color="Maroon" title="c3">x</font> <a href="gaussint.html#R2" title="GAUSSINT:pred.2">is_associated_to</a> <font color="Maroon" title="c5">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:106"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="ref" href="gaussint.html#D20" target="_self" onmouseover="rs('gaussint/D20')" onmouseout="rh()">Def20</a>, <a class="ref" href="gaussint.html#T40" target="_self" onmouseover="rs('gaussint/T40')" onmouseout="rh()">Th40</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/>


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