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<span class="kw">thus </span><a NAME="E1:10_1_1"/>
 <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V3" title="BCIALG_1:attr.3">being_B</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V4" title="BCIALG_1:attr.4">being_C</a>  &amp;  <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V5" title="BCIALG_1:attr.5">being_I</a>  &amp;  <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V7" title="BCIALG_1:attr.7">being_BCI-4</a>  &amp;  <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V8" title="BCIALG_1:attr.8">being_BCK-5</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1_1"><span class="kw">proof </span></a><div class="add">

<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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="bcialg_1.html#D3" target="_self" title="BCIALG_1:def.3">BCIALG_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <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="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a> </span><br/>

<span class="kw">thus </span><a NAME="E1:10_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <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="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E2:10_1_1"/>
 <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V4" title="BCIALG_1:attr.4">being_C</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V5" title="BCIALG_1:attr.5">being_I</a>  &amp;  <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V7" title="BCIALG_1:attr.7">being_BCI-4</a>  &amp;  <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V8" title="BCIALG_1:attr.8">being_BCK-5</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1_2"><span class="kw">proof </span></a><div class="add">

<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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="bcialg_1.html#D4" target="_self" title="BCIALG_1:def.4">BCIALG_1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<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></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><span class="p2">(<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="c3">z</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a> </span><br/>

<span class="kw">thus </span><a NAME="E1:10_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<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></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><span class="p2">(<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="c3">z</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E3:10_1_1"/>
 <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V7" title="BCIALG_1:attr.7">being_BCI-4</a>  &amp;  <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V8" title="BCIALG_1:attr.8">being_BCK-5</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="bcialg_1.html#D5" target="_self" title="BCIALG_1:def.5">BCIALG_1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a> </span><br/>

<span class="kw">thus </span><a NAME="E1:10_1_1_3"/>
<font color="Maroon" title="c1">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E4:10_1_1"/>
 <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V7" title="BCIALG_1:attr.7">being_BCI-4</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V8" title="BCIALG_1:attr.8">being_BCK-5</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="bcialg_1.html#D7" target="_self" title="BCIALG_1:def.7">BCIALG_1:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  &amp; <font color="Maroon" title="c2">y</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> )</span><br/>

<span class="kw">thus </span><a NAME="E1:10_1_1_4"/>
( <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  &amp; <font color="Maroon" title="c2">y</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<a NAME="E5:10_1_1"/>
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  holds  <font color="Olive" title="b1">x</font> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:10_1_1"/>
 <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is  <a href="bcialg_1.html#V8" title="BCIALG_1:attr.8">being_BCK-5</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_1.html#D8" target="_self" title="BCIALG_1:def.8">Def8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
