<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="bcialg_1.html#NM1" title="BCIALG_1:NM.1">BCI-algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I</font> being   <a href="bcialg_1.html#M2" title="BCIALG_1:mode.2">Ideal</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">RI</font> being   <a href="bcialg_2.html#M5" title="BCIALG_2:mode.5">I-congruence</a> of <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">I</font> holds  <font color="Maroon" title="c1">X</font> <a href="bcialg_2.html#K9" title="BCIALG_2:func.9">./.</a> <font color="Olive" title="b2">RI</font> is   <a href="bcialg_1.html#NM1" title="BCIALG_1:NM.1">BCI-algebra</a></span><br/><b>let </b><font color="Maroon" title="c2">I</font> be    <a href="bcialg_1.html#M2" title="BCIALG_1:mode.2">Ideal</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">RI</font> being   <a href="bcialg_2.html#M5" title="BCIALG_2:mode.5">I-congruence</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">I</font> holds  <font color="Maroon" title="c1">X</font> <a href="bcialg_2.html#K9" title="BCIALG_2:func.9">./.</a> <font color="Olive" title="b1">RI</font> is   <a href="bcialg_1.html#NM1" title="BCIALG_1:NM.1">BCI-algebra</a></span><br/><b>let </b><font color="Maroon" title="c3">RI</font> be    <a href="bcialg_2.html#M5" title="BCIALG_2:mode.5">I-congruence</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">I</font>; <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_2.html#K9" title="BCIALG_2:func.9">./.</a> <font color="Maroon" title="c3">RI</font> is   <a href="bcialg_1.html#NM1" title="BCIALG_1:NM.1">BCI-algebra</a></span><br/>





<b>reconsider </b><font color="Maroon" title="c4">IT</font> = <font color="Maroon" title="c1">X</font> <a href="bcialg_2.html#K9" title="BCIALG_2:func.9">./.</a> <font color="Maroon" title="c3">RI</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="bcialg_1.html#L2" title="BCIALG_1:struct.2">BCIStr_0</a>  ;<br/>
<a NAME="E2:77"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon" title="c4">IT</font> is <a href="bcialg_1.html#V3" title="BCIALG_1:attr.3">being_B</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">w1</font>, <font color="Maroon" title="c6">w2</font>, <font color="Maroon" title="c7">w3</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">IT</font>; <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"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</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="c7">w3</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</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="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</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> <font color="Maroon" title="c4">IT</font></span><br/><a NAME="E1:77_1_1"/><i><font color="Green" title="E37">A2</font></i>: 
( <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">IT</font> &amp; <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">IT</font> &amp; <font color="Maroon" title="c7">w3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">IT</font> )
 ;<br/><b>then consider </b><font color="Maroon" title="c8">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:77_1_1"/><i><font color="Green" title="E38">A3</font></i>: 
( <font color="Maroon" title="c8">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<font color="Maroon" title="c8">x1</font> )
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/><b>consider </b><font color="Maroon" title="c9">y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:77_1_1"/><i><font color="Green" title="E39">A4</font></i>: 
( <font color="Maroon" title="c9">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<font color="Maroon" title="c9">y1</font> )
 <b>by </b><i><a class="txt" href="#E1:77_1_1"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/><b>consider </b><font color="Maroon" title="c10">z1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:77_1_1"/><i><font color="Green" title="E40">A5</font></i>: 
( <font color="Maroon" title="c10">z1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c7">w3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<font color="Maroon" title="c10">z1</font> )
 <b>by </b><i><a class="txt" href="#E1:77_1_1"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">x1</font> = <font color="Maroon" title="c8">x1</font>, <font color="Maroon" title="c12">y1</font> = <font color="Maroon" title="c9">y1</font>, <font color="Maroon" title="c13">z1</font> = <font color="Maroon" title="c10">z1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="#E3:77_1_1"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="#E5:77_1_1"><i><font color="Green" title="E39">A4</font></i></a>, <a class="txt" href="#E7:77_1_1"><i><font color="Green" title="E40">A5</font></i></a></i>;<br/><a NAME="E9:77_1_1"/><i><font color="Green" title="E41">A6</font></i>: 
( <font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c12">y1</font></span>)</span> &amp; <font color="Maroon" title="c7">w3</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c13">z1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c12">y1</font></span>)</span> &amp; <font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c13">z1</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E3:77_1_1"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="#E5:77_1_1"><i><font color="Green" title="E39">A4</font></i></a>, <a class="txt" href="#E7:77_1_1"><i><font color="Green" title="E40">A5</font></i></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></i>;<br/><a NAME="E10:77_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">w3</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c12">y1</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="c13">z1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c12">y1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></i>;<br/><a NAME="E11:77_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</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="c7">w3</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</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="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c12">y1</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">z1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c12">y1</font></span>)</span></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c13">z1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="#E9:77_1_1"><i><font color="Green" title="E41">A6</font></i></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></i>;<br/><b>hence </b><a NAME="E12:77_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</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="c7">w3</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</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="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</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> <font color="Maroon" title="c4">IT</font>
 <b>by </b><i><a class="ref" href="bcialg_1.html#D3" title="BCIALG_1:def.3">BCIALG_1:def 3</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>hence </b><a NAME="E2:77_1"/>
<font color="Maroon" title="c4">IT</font> is <a href="bcialg_1.html#V3" title="BCIALG_1:attr.3">being_B</a>
 <b>by </b><i><a class="ref" href="bcialg_1.html#D3" title="BCIALG_1:def.3">BCIALG_1:def 3</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>
<a NAME="E3:77"/><i><font color="Green" title="E37">A7</font></i>: 
<font color="Maroon" title="c4">IT</font> is <a href="bcialg_1.html#V4" title="BCIALG_1:attr.4">being_C</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_2"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">w1</font>, <font color="Maroon" title="c6">w2</font>, <font color="Maroon" title="c7">w3</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">IT</font>; <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"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</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="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</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> <font color="Maroon" title="c4">IT</font></span><br/><a NAME="E1:77_2_1"/><i><font color="Green" title="E38">A8</font></i>: 
( <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">IT</font> &amp; <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">IT</font> &amp; <font color="Maroon" title="c7">w3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">IT</font> )
 ;<br/><b>then consider </b><font color="Maroon" title="c8">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:77_2_1"/><i><font color="Green" title="E39">A9</font></i>: 
( <font color="Maroon" title="c8">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<font color="Maroon" title="c8">x1</font> )
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/><b>consider </b><font color="Maroon" title="c9">y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:77_2_1"/><i><font color="Green" title="E40">A10</font></i>: 
( <font color="Maroon" title="c9">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<font color="Maroon" title="c9">y1</font> )
 <b>by </b><i><a class="txt" href="#E1:77_2_1"><i><font color="Green" title="E38">A8</font></i></a>, <a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/><b>consider </b><font color="Maroon" title="c10">z1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:77_2_1"/><i><font color="Green" title="E41">A11</font></i>: 
( <font color="Maroon" title="c10">z1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c7">w3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<font color="Maroon" title="c10">z1</font> )
 <b>by </b><i><a class="txt" href="#E1:77_2_1"><i><font color="Green" title="E38">A8</font></i></a>, <a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">x1</font> = <font color="Maroon" title="c8">x1</font>, <font color="Maroon" title="c12">y1</font> = <font color="Maroon" title="c9">y1</font>, <font color="Maroon" title="c13">z1</font> = <font color="Maroon" title="c10">z1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="#E3:77_2_1"><i><font color="Green" title="E39">A9</font></i></a>, <a class="txt" href="#E5:77_2_1"><i><font color="Green" title="E40">A10</font></i></a>, <a class="txt" href="#E7:77_2_1"><i><font color="Green" title="E41">A11</font></i></a></i>;<br/><a NAME="E9:77_2_1"/>
( <font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c12">y1</font></span>)</span> &amp; <font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c13">z1</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E3:77_2_1"><i><font color="Green" title="E39">A9</font></i></a>, <a class="txt" href="#E5:77_2_1"><i><font color="Green" title="E40">A10</font></i></a>, <a class="txt" href="#E7:77_2_1"><i><font color="Green" title="E41">A11</font></i></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></i>;<br/><a NAME="E10:77_2_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c12">y1</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c13">z1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c13">z1</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c12">y1</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E5:77_2_1"><i><font color="Green" title="E40">A10</font></i></a>, <a class="txt" href="#E7:77_2_1"><i><font color="Green" title="E41">A11</font></i></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></i>;<br/><a NAME="E11:77_2_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</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="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c12">y1</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c13">z1</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c13">z1</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c12">y1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></i>;<br/><b>hence </b><a NAME="E12:77_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</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="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">w3</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</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> <font color="Maroon" title="c4">IT</font>
 <b>by </b><i><a class="ref" href="bcialg_1.html#D4" title="BCIALG_1:def.4">BCIALG_1:def 4</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>hence </b><a NAME="E2:77_2"/>
<font color="Maroon" title="c4">IT</font> is <a href="bcialg_1.html#V4" title="BCIALG_1:attr.4">being_C</a>
 <b>by </b><i><a class="ref" href="bcialg_1.html#D4" title="BCIALG_1:def.4">BCIALG_1:def 4</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>
<a NAME="E4:77"/><i><font color="Green" title="E38">A12</font></i>: 
<font color="Maroon" title="c4">IT</font> is <a href="bcialg_1.html#V5" title="BCIALG_1:attr.5">being_I</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_3"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">w1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">IT</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">IT</font></span><br/><a NAME="E1:77_3_1"/>
<font color="Maroon" title="c5">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">IT</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c6">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:77_3_1"/><i><font color="Green" title="E39">A13</font></i>: 
( <font color="Maroon" title="c6">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<font color="Maroon" title="c6">x1</font> )
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c7">x1</font> = <font color="Maroon" title="c6">x1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="#E3:77_3_1"><i><font color="Green" title="E39">A13</font></i></a></i>;<br/><a NAME="E5:77_3_1"/>
<font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c7">x1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:77_3_1"><i><font color="Green" title="E39">A13</font></i></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></i>;<br/><b>hence </b><a NAME="E6:77_3_1"/>
<font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">IT</font>
 <b>by </b><i><a class="ref" href="bcialg_1.html#D5" title="BCIALG_1:def.5">BCIALG_1:def 5</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>hence </b><a NAME="E2:77_3"/>
<font color="Maroon" title="c4">IT</font> is <a href="bcialg_1.html#V5" title="BCIALG_1:attr.5">being_I</a>
 <b>by </b><i><a class="ref" href="bcialg_1.html#D5" title="BCIALG_1:def.5">BCIALG_1:def 5</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>
<a NAME="E5:77"/>
<font color="Maroon" title="c4">IT</font> is <a href="bcialg_1.html#V7" title="BCIALG_1:attr.7">being_BCI-4</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_4"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">w1</font>, <font color="Maroon" title="c6">w2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">IT</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">IT</font> &amp; <font color="Maroon" title="c6">w2</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">IT</font> implies <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">w2</font> )</span><br/><b>assume </b><a NAME="E1:77_4_1"/><i><font color="Green" title="E39">A14</font></i>: 
( <font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">IT</font> &amp; <font color="Maroon" title="c6">w2</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">IT</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">w2</font></span><br/><a NAME="E2:77_4_1"/><i><font color="Green" title="E40">A15</font></i>: 
( <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">IT</font> &amp; <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">IT</font> )
 ;<br/><b>then consider </b><font color="Maroon" title="c7">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:77_4_1"/><i><font color="Green" title="E41">A16</font></i>: 
( <font color="Maroon" title="c7">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<font color="Maroon" title="c7">x1</font> )
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/><b>consider </b><font color="Maroon" title="c8">y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:77_4_1"/><i><font color="Green" title="E42">A17</font></i>: 
( <font color="Maroon" title="c8">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<font color="Maroon" title="c8">y1</font> )
 <b>by </b><i><a class="txt" href="#E2:77_4_1"><i><font color="Green" title="E40">A15</font></i></a>, <a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">x1</font> = <font color="Maroon" title="c7">x1</font>, <font color="Maroon" title="c10">y1</font> = <font color="Maroon" title="c8">y1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="#E4:77_4_1"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="#E6:77_4_1"><i><font color="Green" title="E42">A17</font></i></a></i>;<br/><a NAME="E8:77_4_1"/>
( <font color="Maroon" title="c5">w1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c6">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c10">y1</font></span>)</span> &amp; <font color="Maroon" title="c6">w2</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">y1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c9">x1</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E4:77_4_1"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="#E6:77_4_1"><i><font color="Green" title="E42">A17</font></i></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></i>;<br/><a NAME="E9:77_4_1"/><b>then </b>
(  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c10">y1</font></span>)</span> &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <font color="Maroon" title="c3">RI</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">y1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c9">x1</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E1:77_4_1"><i><font color="Green" title="E39">A14</font></i></a>, <a class="ref" href="eqrel_1.html#T31" title="EQREL_1:th.31">EQREL_1:31</a></i>;<br/><a NAME="E10:77_4_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c10">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">RI</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">y1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c9">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">RI</font> )
 <b>by </b><i><a class="ref" href="eqrel_1.html#T26" title="EQREL_1:th.26">EQREL_1:26</a></i>;<br/><a NAME="E11:77_4_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c9">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c10">y1</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">I</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c10">y1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c9">x1</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">I</font> )
 <b>by </b><i><a class="ref" href="bcialg_2.html#D12" target="_self" title="BCIALG_2:def.12">Def12</a></i>;<br/><a NAME="E12:77_4_1"/><b>then </b>
( <font color="Maroon" title="c9">x1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c10">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">I</font> &amp; <font color="Maroon" title="c10">y1</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c9">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">I</font> )
 <b>by </b><i><a class="ref" href="bcialg_1.html#T2" title="BCIALG_1:th.2">BCIALG_1:2</a></i>;<br/><a NAME="E13:77_4_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">x1</font>,<font color="Maroon" title="c10">y1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">RI</font>
 <b>by </b><i><a class="ref" href="bcialg_2.html#D12" target="_self" title="BCIALG_2:def.12">Def12</a></i>;<br/><b>hence </b><a NAME="E14:77_4_1"/>
<font color="Maroon" title="c5">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">w2</font>
 <b>by </b><i><a class="txt" href="#E4:77_4_1"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="#E6:77_4_1"><i><font color="Green" title="E42">A17</font></i></a>, <a class="ref" href="eqrel_1.html#T44" title="EQREL_1:th.44">EQREL_1:44</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>hence </b><a NAME="E2:77_4"/>
<font color="Maroon" title="c4">IT</font> is <a href="bcialg_1.html#V7" title="BCIALG_1:attr.7">being_BCI-4</a>
 <b>by </b><i><a class="ref" href="bcialg_1.html#D7" title="BCIALG_1:def.7">BCIALG_1:def 7</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>hence </b><a NAME="E6:77"/>
<font color="Maroon" title="c1">X</font> <a href="bcialg_2.html#K9" title="BCIALG_2:func.9">./.</a> <font color="Maroon" title="c3">RI</font> is   <a href="bcialg_1.html#NM1" title="BCIALG_1:NM.1">BCI-algebra</a>
 <b>by </b><i><a class="txt" href="#E2:77"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="#E3:77"><i><font color="Green" title="E37">A7</font></i></a>, <a class="txt" href="#E4:77"><i><font color="Green" title="E38">A12</font></i></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>
