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<b>thus </b><a NAME="E1:74"/>
 <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_4.html#V5" title="BCIALG_4:attr.5">being_SB-1</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_4.html#V6" title="BCIALG_4:attr.6">being_SB-2</a> &amp;  <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_4.html#V7" title="BCIALG_4:attr.7">being_SB-4</a> &amp;  <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_1.html#V5" title="BCIALG_1:attr.5">being_I</a> &amp;  <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_4.html#V2" title="BCIALG_4:attr.2">with_condition_S</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="bcialg_4.html#D12" target="_self" title="BCIALG_4:def.12">BCIALG_4:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">x</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font></span><br/>

<b>thus </b><a NAME="E1:74_1"/>
<font color="Maroon" title="c1">x</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font>
 <b>by </b><i><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:74"/>
 <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_4.html#V6" title="BCIALG_4:attr.6">being_SB-2</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_4.html#V7" title="BCIALG_4:attr.7">being_SB-4</a> &amp;  <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_1.html#V5" title="BCIALG_1:attr.5">being_I</a> &amp;  <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_4.html#V2" title="BCIALG_4:attr.2">with_condition_S</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="bcialg_4.html#D13" target="_self" title="BCIALG_4:def.13">BCIALG_4:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">x</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c1">x</font></span><br/>

<b>thus </b><a NAME="E1:74_2"/>
<font color="Maroon" title="c1">x</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c1">x</font>
 <b>by </b><i><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:74"/>
 <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_4.html#V7" title="BCIALG_4:attr.7">being_SB-4</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_1.html#V5" title="BCIALG_1:attr.5">being_I</a> &amp;  <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_4.html#V2" title="BCIALG_4:attr.2">with_condition_S</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="bcialg_4.html#D14" target="_self" title="BCIALG_4:def.14">BCIALG_4:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c2">y</font></span><br/>

<b>thus </b><a NAME="E1:74_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c2">y</font>
 <b>by </b><i><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:74"/>
 <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_1.html#V5" title="BCIALG_1:attr.5">being_I</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  is <a href="bcialg_4.html#V2" title="BCIALG_4:attr.2">with_condition_S</a></span><br/>

<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="bcialg_4.html#D2" target="_self" title="BCIALG_4:def.2">BCIALG_4:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c3">z</font></span>)</span></span><br/>

<b>thus </b><a NAME="E5:74"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c3">z</font></span>)</span>
 <b>by </b><i><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
