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<span class="kw">set </span><font color="Maroon" title="c3">E</font> =  <a href="ring_1.html#K1" title="RING_1:func.1">EqRel</a> (<font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">I</font>);<br/>
<span class="kw">let </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <font color="Maroon" title="c2">I</font></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="group_1.html#D12" onmouseover="rs('group_1/D12')" onmouseout="rh()">GROUP_1:def 12</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="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c6">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E2:31_1_1"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ring_1.html#K1" title="RING_1:func.1">EqRel</a> (<font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">I</font>)</span>)</span>,<font color="Maroon" title="c6">a</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ring_1.html#T11" target="_self" onmouseover="rs('ring_1/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E4:31_1_1"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ring_1.html#K1" title="RING_1:func.1">EqRel</a> (<font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">I</font>)</span>)</span>,<font color="Maroon" title="c7">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ring_1.html#T11" target="_self" onmouseover="rs('ring_1/T11')" onmouseout="rh()">Th11</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font> = 
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ring_1.html#K1" title="RING_1:func.1">EqRel</a> (<font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">I</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">b</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31_1_1"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E4:31_1_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="ring_1.html#T14" target="_self" onmouseover="rs('ring_1/T14')" onmouseout="rh()">Th14</a></span>
<br/>.= 
<font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:31_1_1"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E4:31_1_1"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="ring_1.html#T14" target="_self" onmouseover="rs('ring_1/T14')" onmouseout="rh()">Th14</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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