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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>





<span class="kw">reconsider </span><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/>
<div><span class="lab"><font color="Green" title="E36">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"/>
<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/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:77_1"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E4:77_1"/><span class="lab"><font color="Green" title="E38">A3</font></span>: 
<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>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></span>;<br/><a NAME="E5:77_1"/>
<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/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">z1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E7:77_1"/><span class="lab"><font color="Green" title="E39">A4</font></span>: 
<font color="Maroon" title="c9">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>
 <span class="kw">and </span><br/><a NAME="E8:77_1"/><span class="lab"><font color="Green" title="E40">A5</font></span>: 
<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="c9">z1</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></span>;<br/><a NAME="E9:77_1"/>
<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/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E11:77_1"/><span class="lab"><font color="Green" title="E41">A6</font></span>: 
<font color="Maroon" title="c10">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>
 <span class="kw">and </span><br/><a NAME="E12:77_1"/><span class="lab"><font color="Green" title="E42">A7</font></span>: 
<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="c10">y1</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></span>;<br/><span class="kw">reconsider </span><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="c10">y1</font>, <font color="Maroon" title="c13">z1</font> = <font color="Maroon" title="c9">z1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:77_1"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E11:77_1"><span class="lab"><font color="Green" title="E41">A6</font></span></a>, <a class="txt" href="#E7:77_1"><span class="lab"><font color="Green" title="E39">A4</font></span></a></span>;<br/><a NAME="E14:77_1"/><span class="lab"><font color="Green" title="E43">A8</font></span>: 
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:77_1"><span class="lab"><font color="Green" title="E42">A7</font></span></a>, <a class="txt" href="#E8:77_1"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><a NAME="E15:77_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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:77_1"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="txt" href="#E12:77_1"><span class="lab"><font color="Green" title="E42">A7</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><a NAME="E16:77_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A9</font></span>: 
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:77_1"><span class="lab"><font color="Green" title="E43">A8</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><a NAME="E17:77_1"/>
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:77_1"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="txt" href="#E8:77_1"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><a NAME="E18:77_1"/><span class="kw">then </span>
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:77_1"><span class="lab"><font color="Green" title="E44">A9</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><span class="kw">hence </span><a NAME="E19:77_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_1.html#D3" title="BCIALG_1:def.3">BCIALG_1:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E37">A10</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="77_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"/>
<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/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:77_2"/><span class="lab"><font color="Green" title="E38">A11</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E4:77_2"/><span class="lab"><font color="Green" title="E39">A12</font></span>: 
<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>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></span>;<br/><a NAME="E5:77_2"/>
<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/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E7:77_2"/><span class="lab"><font color="Green" title="E40">A13</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E8:77_2"/><span class="lab"><font color="Green" title="E41">A14</font></span>: 
<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>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></span>;<br/><a NAME="E9:77_2"/>
<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/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">z1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E11:77_2"/><span class="lab"><font color="Green" title="E42">A15</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E12:77_2"/><span class="lab"><font color="Green" title="E43">A16</font></span>: 
<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>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></span>;<br/><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:77_2"><span class="lab"><font color="Green" title="E38">A11</font></span></a>, <a class="txt" href="#E7:77_2"><span class="lab"><font color="Green" title="E40">A13</font></span></a>, <a class="txt" href="#E11:77_2"><span class="lab"><font color="Green" title="E42">A15</font></span></a></span>;<br/><a NAME="E14:77_2"/>
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:77_2"><span class="lab"><font color="Green" title="E39">A12</font></span></a>, <a class="txt" href="#E12:77_2"><span class="lab"><font color="Green" title="E43">A16</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><a NAME="E15:77_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A17</font></span>: 
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:77_2"><span class="lab"><font color="Green" title="E41">A14</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><a NAME="E16:77_2"/>
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:77_2"><span class="lab"><font color="Green" title="E39">A12</font></span></a>, <a class="txt" href="#E8:77_2"><span class="lab"><font color="Green" title="E41">A14</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><a NAME="E17:77_2"/><span class="kw">then </span>
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:77_2"><span class="lab"><font color="Green" title="E43">A16</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><a NAME="E18:77_2"/><span class="kw">then </span>
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:77_2"><span class="lab"><font color="Green" title="E44">A17</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><span class="kw">hence </span><a NAME="E19:77_2"/>
<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 class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_1.html#D4" title="BCIALG_1:def.4">BCIALG_1:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E38">A18</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="77_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:77_3"/><span class="lab"><font color="Green" title="E39">A19</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:77_3"/><span class="lab"><font color="Green" title="E40">A20</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E3:77_3"/>
<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/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E5:77_3"/><span class="lab"><font color="Green" title="E41">A21</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E6:77_3"/><span class="lab"><font color="Green" title="E42">A22</font></span>: 
<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>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></span>;<br/><a NAME="E7:77_3"/>
<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/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E9:77_3"/><span class="lab"><font color="Green" title="E43">A23</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E10:77_3"/><span class="lab"><font color="Green" title="E44">A24</font></span>: 
<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>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></span>;<br/><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:77_3"><span class="lab"><font color="Green" title="E41">A21</font></span></a>, <a class="txt" href="#E9:77_3"><span class="lab"><font color="Green" title="E43">A23</font></span></a></span>;<br/><a NAME="E12:77_3"/>
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:77_3"><span class="lab"><font color="Green" title="E42">A22</font></span></a>, <a class="txt" href="#E10:77_3"><span class="lab"><font color="Green" title="E44">A24</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><a NAME="E13:77_3"/><span class="kw">then </span>
 <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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:77_3"><span class="lab"><font color="Green" title="E40">A20</font></span></a>, <a class="ref" href="eqrel_1.html#T23" title="EQREL_1:th.23">EQREL_1:23</a></span>;<br/><a NAME="E14:77_3"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T18" title="EQREL_1:th.18">EQREL_1:18</a></span>;<br/><a NAME="E15:77_3"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_2.html#D12" target="_self" title="BCIALG_2:def.12">Def12</a></span>;<br/><a NAME="E16:77_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A25</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_1.html#T2" title="BCIALG_1:th.2">BCIALG_1:2</a></span>;<br/><a NAME="E17:77_3"/>
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:77_3"><span class="lab"><font color="Green" title="E42">A22</font></span></a>, <a class="txt" href="#E10:77_3"><span class="lab"><font color="Green" title="E44">A24</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><a NAME="E18:77_3"/><span class="kw">then </span>
 <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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:77_3"><span class="lab"><font color="Green" title="E39">A19</font></span></a>, <a class="ref" href="eqrel_1.html#T23" title="EQREL_1:th.23">EQREL_1:23</a></span>;<br/><a NAME="E19:77_3"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T18" title="EQREL_1:th.18">EQREL_1:18</a></span>;<br/><a NAME="E20:77_3"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_2.html#D12" target="_self" title="BCIALG_2:def.12">Def12</a></span>;<br/><a NAME="E21:77_3"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_1.html#T2" title="BCIALG_1:th.2">BCIALG_1:2</a></span>;<br/><a NAME="E22:77_3"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:77_3"><span class="lab"><font color="Green" title="E45">A25</font></span></a>, <a class="ref" href="bcialg_2.html#D12" target="_self" title="BCIALG_2:def.12">Def12</a></span>;<br/><span class="kw">hence </span><a NAME="E23:77_3"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E6:77_3"><span class="lab"><font color="Green" title="E42">A22</font></span></a>, <a class="txt" href="#E10:77_3"><span class="lab"><font color="Green" title="E44">A24</font></span></a>, <a class="ref" href="eqrel_1.html#T35" title="EQREL_1:th.35">EQREL_1:35</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_4"/>
<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/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:77_4"/><span class="lab"><font color="Green" title="E39">A26</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E4:77_4"/><span class="lab"><font color="Green" title="E40">A27</font></span>: 
<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>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D3" title="EQREL_1:def.3">EQREL_1:def 3</a></span>;<br/><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:77_4"><span class="lab"><font color="Green" title="E39">A26</font></span></a></span>;<br/><a NAME="E6:77_4"/>
<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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:77_4"><span class="lab"><font color="Green" title="E40">A27</font></span></a>, <a class="ref" href="bcialg_2.html#D17" target="_self" title="BCIALG_2:def.17">Def17</a></span>;<br/><span class="kw">hence </span><a NAME="E7:77_4"/>
<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 class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_1.html#D5" title="BCIALG_1:def.5">BCIALG_1:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:77"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E3:77"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="txt" href="#E4:77"><span class="lab"><font color="Green" title="E38">A18</font></span></a>, <a class="ref" href="bcialg_1.html#D3" title="BCIALG_1:def.3">BCIALG_1:def 3</a>, <a class="ref" href="bcialg_1.html#D4" title="BCIALG_1:def.4">BCIALG_1:def 4</a>, <a class="ref" href="bcialg_1.html#D5" title="BCIALG_1:def.5">BCIALG_1:def 5</a>, <a class="ref" href="bcialg_1.html#D7" title="BCIALG_1:def.7">BCIALG_1:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
