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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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b2">m</font>, <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">x</font> is  <a href="bcialg_6.html#V1" title="BCIALG_6:attr.1">finite-period</a>  &amp;  <a href="bcialg_6.html#K3" title="BCIALG_6:func.3">ord</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">n</font> holds <br/>( <font color="Olive" title="b1">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Olive" title="b2">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font> iff <font color="Olive" title="b3">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Olive" title="b2">m</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Maroon" title="c2">x</font> is  <a href="bcialg_6.html#V1" title="BCIALG_6:attr.1">finite-period</a>  &amp;  <a href="bcialg_6.html#K3" title="BCIALG_6:func.3">ord</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">n</font> holds <br/>( <font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Olive" title="b1">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font> iff <font color="Olive" title="b2">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Olive" title="b1">m</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c4">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> is  <a href="bcialg_6.html#V1" title="BCIALG_6:attr.1">finite-period</a>  &amp;  <a href="bcialg_6.html#K3" title="BCIALG_6:func.3">ord</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> implies ( <font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font> iff <font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c3">m</font> ) )</span><br/>







<span class="kw">reconsider </span><font color="Maroon" title="c5">b</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bcialg_1.html#K5" title="BCIALG_1:func.5">AtomSet</a> <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_1.html#T34" onmouseover="rs('bcialg_1/T34')" onmouseout="rh()">BCIALG_1:34</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">bn</font> = <font color="Maroon" title="c5">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c4">n</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bcialg_1.html#K5" title="BCIALG_1:func.5">AtomSet</a> <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_6.html#T13" target="_self" onmouseover="rs('bcialg_6/T13')" onmouseout="rh()">Th13</a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:35"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
<font color="Maroon" title="c2">x</font> is  <a href="bcialg_6.html#V1" title="BCIALG_6:attr.1">finite-period</a> 
 <span class="kw">and </span><br/><a NAME="E4:35"/><span class="lab"><font color="Green" title="E29">A2</font></span>: 
 <a href="bcialg_6.html#K3" title="BCIALG_6:func.3">ord</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font> iff <font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c3">m</font> )</span><br/>

<a NAME="E5:35"/><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<font color="Maroon" title="c5">b</font> is  <a href="bcialg_6.html#V1" title="BCIALG_6:attr.1">finite-period</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="bcialg_6.html#T25" target="_self" onmouseover="rs('bcialg_6/T25')" onmouseout="rh()">Th25</a></span>;<br/>
<span class="kw">thus </span><a NAME="E6:35"/>
( <font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c3">m</font> )
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c3">m</font> implies <font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="35_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>] <span class="kw">means </span>( <font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> $1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> $1 );<br/>
<a NAME="E1:35_1"/><span class="lab"><font color="Green" title="E31">A4</font></span>: 
 for <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st (  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">m</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">k</font>] ) holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>]
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="35_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">m</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">m</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] ) implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">m</font>] )</span><br/>

<span class="kw">assume </span><a NAME="E1:35_1_1"/><span class="lab"><font color="Green" title="E32">A5</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">m</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">m</font>]</span><br/>

<span class="kw">assume </span><a NAME="E2:35_1_1"/><span class="lab"><font color="Green" title="E33">A6</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c7">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c7">m</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:35_1_1_1"/>
( <font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c7">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:35_1_1_1_1"/>
<font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c7">m</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:35_1_1_1_1"/>
<font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c7">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#T12" onmouseover="rs('int_2/T12')" onmouseout="rh()">INT_2:12</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:35_1_1_1_2"/><span class="lab"><font color="Green" title="E34">A7</font></span>: 
<font color="Maroon" title="c7">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c7">m</font></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c8">mm</font> = <font color="Maroon" title="c7">m</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" onmouseover="rs('ordinal1/D12')" onmouseout="rh()">ORDINAL1:def 12</a></span>;<br/><a NAME="E3:35_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c8">mm</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35_1_1"><span class="lab"><font color="Green" title="E33">A6</font></span></a></span>;<br/><a NAME="E4:35_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E4:35"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="txt" href="#E1:35_1_1_1_2"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="ref" href="bcialg_6.html#D5" target="_self" onmouseover="rs('bcialg_6/D5')" onmouseout="rh()">Def5</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E6:35_1_1_1_2"/><span class="lab"><font color="Green" title="E35">A8</font></span>: 
<font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c9">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" onmouseover="rs('nat_1/T10')" onmouseout="rh()">NAT_1:10</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c10">b</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bcialg_1.html#K5" title="BCIALG_1:func.5">AtomSet</a> <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_1.html#T34" onmouseover="rs('bcialg_1/T34')" onmouseout="rh()">BCIALG_1:34</a></span>;<br/><a NAME="E8:35_1_1_1_2"/><span class="lab"><font color="Green" title="E36">A9</font></span>: 
<font color="Maroon" title="c10">b</font> is  <a href="bcialg_6.html#V1" title="BCIALG_6:attr.1">finite-period</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="bcialg_6.html#T25" target="_self" onmouseover="rs('bcialg_6/T25')" onmouseout="rh()">Th25</a></span>;<br/><a NAME="E9:35_1_1_1_2"/>
<font color="Maroon" title="c10">b</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_1.html#T1" onmouseover="rs('bcialg_1/T1')" onmouseout="rh()">BCIALG_1:1</a></span>;<br/><a NAME="E10:35_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">b</font> <a href="bcialg_1.html#R1" title="BCIALG_1:pred.1">&lt;=</a> <font color="Maroon" title="c2">x</font>
 ;<br/><a NAME="E11:35_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K7" title="BCIALG_1:func.7">BranchV</a> <font color="Maroon" title="c10">b</font>
 ;<br/><a NAME="E12:35_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bcialg_6.html#K3" title="BCIALG_6:func.3">ord</a> <font color="Maroon" title="c10">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E4:35"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="txt" href="#E8:35_1_1_1_2"><span class="lab"><font color="Green" title="E36">A9</font></span></a>, <a class="ref" href="bcialg_6.html#T28" target="_self" onmouseover="rs('bcialg_6/T28')" onmouseout="rh()">Th28</a></span>;<br/><a NAME="E13:35_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c4">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:35_1_1_1_2"><span class="lab"><font color="Green" title="E36">A9</font></span></a>, <a class="ref" href="bcialg_6.html#D5" target="_self" onmouseover="rs('bcialg_6/D5')" onmouseout="rh()">Def5</a></span>;<br/><a NAME="E14:35_1_1_1_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c4">n</font> &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> <a href="bcialg_1.html#R1" title="BCIALG_1:pred.1">&lt;=</a> <font color="Olive" title="b1">z</font> )
 ;<br/><a NAME="E15:35_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A10</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 ;<br/><a NAME="E16:35_1_1_1_2"/>
 ex <font color="Olive" title="b1">zz</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">zz</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c7">m</font> &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> <a href="bcialg_1.html#R1" title="BCIALG_1:pred.1">&lt;=</a> <font color="Olive" title="b1">zz</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:35_1_1"><span class="lab"><font color="Green" title="E33">A6</font></span></a></span>;<br/><a NAME="E17:35_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c7">m</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 ;<br/><a NAME="E18:35_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c10">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:35_1_1_1_2"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="ref" href="bcialg_6.html#T21" target="_self" onmouseover="rs('bcialg_6/T21')" onmouseout="rh()">Th21</a></span>;<br/><a NAME="E19:35_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c4">n</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="c10">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a></span>)</span></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_6.html#T24" target="_self" onmouseover="rs('bcialg_6/T24')" onmouseout="rh()">Th24</a></span>;<br/><a NAME="E20:35_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:35_1_1_1_2"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="ref" href="bcialg_1.html#T9" onmouseover="rs('bcialg_1/T9')" onmouseout="rh()">BCIALG_1:9</a></span>;<br/><a NAME="E21:35_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c10">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_1.html#T8" onmouseover="rs('bcialg_1/T8')" onmouseout="rh()">BCIALG_1:8</a></span>;<br/><a NAME="E22:35_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_6.html#T21" target="_self" onmouseover="rs('bcialg_6/T21')" onmouseout="rh()">Th21</a></span>;<br/><a NAME="E23:35_1_1_1_2"/><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="bcialg_1.html#R1" title="BCIALG_1:pred.1">&lt;=</a> <font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c9">k</font>
 ;<br/><a NAME="E24:35_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A11</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c9">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font>
 ;<br/><a NAME="E25:35_1_1_1_2"/>
<font color="Maroon" title="c4">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E4:35"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="bcialg_6.html#D5" target="_self" onmouseover="rs('bcialg_6/D5')" onmouseout="rh()">Def5</a></span>;<br/><a NAME="E26:35_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c9">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35_1_1"><span class="lab"><font color="Green" title="E32">A5</font></span></a>, <a class="txt" href="#E6:35_1_1_1_2"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="txt" href="#E24:35_1_1_1_2"><span class="lab"><font color="Green" title="E38">A11</font></span></a>, <a class="ref" href="nat_1.html#T16" onmouseover="rs('nat_1/T16')" onmouseout="rh()">NAT_1:16</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E28:35_1_1_1_2"/><span class="lab"><font color="Green" title="E39">A12</font></span>: 
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c11">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D3" onmouseover="rs('nat_d/D3')" onmouseout="rh()">NAT_D:def 3</a></span>;<br/><a NAME="E29:35_1_1_1_2"/>
<font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c11">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:35_1_1_1_2"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="txt" href="#E28:35_1_1_1_2"><span class="lab"><font color="Green" title="E39">A12</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E30:35_1_1_1_2"/>
<font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c7">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D3" onmouseover="rs('nat_d/D3')" onmouseout="rh()">NAT_D:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E2:35_1"/>
 for <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S4" onmouseover="rs('nat_1/S4')" onmouseout="rh()">NAT_1:sch 4</a>(<a class="txt" href="#E1:35_1"><span class="lab"><font color="Green" title="E31">A4</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E3:35_1"/>
( <font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c3">m</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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

<span class="kw">assume </span><a NAME="E7:35"/>
<font color="Maroon" title="c4">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c3">m</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E9:35"/><span class="lab"><font color="Green" title="E31">A13</font></span>: 
<font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c7">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D3" onmouseover="rs('nat_d/D3')" onmouseout="rh()">NAT_D:def 3</a></span>;<br/>
<a NAME="E10:35"/>
<font color="Maroon" title="c5">b</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_1.html#T1" onmouseover="rs('bcialg_1/T1')" onmouseout="rh()">BCIALG_1:1</a></span>;<br/>
<a NAME="E11:35"/><span class="kw">then </span>
<font color="Maroon" title="c5">b</font> <a href="bcialg_1.html#R1" title="BCIALG_1:pred.1">&lt;=</a> <font color="Maroon" title="c2">x</font>
 
;<br/>
<a NAME="E12:35"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K7" title="BCIALG_1:func.7">BranchV</a> <font color="Maroon" title="c5">b</font>
 
;<br/>
<a NAME="E13:35"/><span class="kw">then </span>
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bcialg_6.html#K3" title="BCIALG_6:func.3">ord</a> <font color="Maroon" title="c5">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E4:35"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="txt" href="#E5:35"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="ref" href="bcialg_6.html#T28" target="_self" onmouseover="rs('bcialg_6/T28')" onmouseout="rh()">Th28</a></span>;<br/>
<a NAME="E14:35"/><span class="kw">then </span>
<font color="Maroon" title="c5">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c4">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:35"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="ref" href="bcialg_6.html#D5" target="_self" onmouseover="rs('bcialg_6/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<a NAME="E15:35"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c4">n</font> &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> <a href="bcialg_1.html#R1" title="BCIALG_1:pred.1">&lt;=</a> <font color="Olive" title="b1">z</font> )
 
;<br/>
<a NAME="E16:35"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A14</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 
;<br/>
<a NAME="E17:35"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">bn</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:35"><span class="lab"><font color="Green" title="E31">A13</font></span></a>, <a class="ref" href="bcialg_6.html#T23" target="_self" onmouseover="rs('bcialg_6/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<a NAME="E18:35"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.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="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c7">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:35"><span class="lab"><font color="Green" title="E32">A14</font></span></a>, <a class="ref" href="bcialg_6.html#T17" target="_self" onmouseover="rs('bcialg_6/T17')" onmouseout="rh()">Th17</a></span>;<br/>
<a NAME="E19:35"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_6.html#T7" target="_self" onmouseover="rs('bcialg_6/T7')" onmouseout="rh()">Th7</a></span>;<br/>
<a NAME="E20:35"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="bcialg_1.html#K2" title="BCIALG_1:func.2">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_6.html#T21" target="_self" onmouseover="rs('bcialg_6/T21')" onmouseout="rh()">Th21</a></span>;<br/>
<a NAME="E21:35"/><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="bcialg_1.html#R1" title="BCIALG_1:pred.1">&lt;=</a> <font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E22:35"/>
<font color="Maroon" title="c2">x</font> <a href="bcialg_6.html#K2" title="BCIALG_6:func.2">|^</a> <font color="Maroon" title="c3">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bcialg_1.html#K4" title="BCIALG_1:func.4">BCK-part</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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