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<div><span class="kw">hereby </span> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="prob_2.html#D2" onmouseover="rs('prob_2/D2')" onmouseout="rh()">PROB_2:def 2</a>,<a class="ref" href="msafree1.html#D2" onmouseover="rs('msafree1/D2')" onmouseout="rh()">MSAFREE1:def 2</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">  <a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font> is  <a href="msualg_6.html#V1" title="MSUALG_6:attr.1">feasible</a> </span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">y</font> implies  not  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">y</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:67_1_1_1"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">y</font>
 <span class="kw">and </span><br/><a NAME="E2:67_1_1_1"/><span class="lab"><font color="Green" title="E34">A2</font></span>: 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">y</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"> contradiction</span><br/><span class="kw">consider </span><font color="Maroon" title="c4">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E4:67_1_1_1"/><span class="lab"><font color="Green" title="E35">A3</font></span>: 
<font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font>
 <span class="kw">and </span><br/><a NAME="E5:67_1_1_1"/><span class="lab"><font color="Green" title="E36">A4</font></span>: 
<font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67_1_1_1"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="xboole_0.html#T3" onmouseover="rs('xboole_0/T3')" onmouseout="rh()">XBOOLE_0:3</a></span>;<br/><a NAME="E6:67_1_1_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">x</font> = <font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c6">y</font> = <font color="Maroon" title="c3">y</font> as   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67_1_1_1"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="txt" href="#E5:67_1_1_1"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="ref" href="funct_1.html#D2" onmouseover="rs('funct_1/D2')" onmouseout="rh()">FUNCT_1:def 2</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font><span class="kw"> such that </span><br/><a NAME="E9:67_1_1_1"/><span class="lab"><font color="Green" title="E37">A5</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="catalg_1.html#T15" target="_self" onmouseover="rs('catalg_1/T15')" onmouseout="rh()">Th15</a></span>;<br/><a NAME="E10:67_1_1_1"/><span class="lab"><font color="Green" title="E38">A6</font></span>: 
<font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67_1_1_1"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="txt" href="#E9:67_1_1_1"><span class="lab"><font color="Green" title="E37">A5</font></span></a>, <a class="ref" href="catalg_1.html#D13" target="_self" onmouseover="rs('catalg_1/D13')" onmouseout="rh()">Def13</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c9">c</font>, <font color="Maroon" title="c10">d</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font><span class="kw"> such that </span><br/><a NAME="E12:67_1_1_1"/><span class="lab"><font color="Green" title="E39">A7</font></span>: 
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> (<font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">d</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="catalg_1.html#T15" target="_self" onmouseover="rs('catalg_1/T15')" onmouseout="rh()">Th15</a></span>;<br/><a NAME="E13:67_1_1_1"/><span class="lab"><font color="Green" title="E40">A8</font></span>: 
<font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">d</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:67_1_1_1"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="txt" href="#E12:67_1_1_1"><span class="lab"><font color="Green" title="E39">A7</font></span></a>, <a class="ref" href="catalg_1.html#D13" target="_self" onmouseover="rs('catalg_1/D13')" onmouseout="rh()">Def13</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c11">z</font> = <font color="Maroon" title="c4">z</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:67_1_1_1"><span class="lab"><font color="Green" title="E38">A6</font></span></a></span>;<br/><a NAME="E15:67_1_1_1"/><span class="lab"><font color="Green" title="E41">A9</font></span>: 
(  <a href="graph_1.html#K3" title="GRAPH_1:func.3">dom</a> <font color="Maroon" title="c11">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a</font> &amp;  <a href="graph_1.html#K4" title="GRAPH_1:func.4">cod</a> <font color="Maroon" title="c11">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:67_1_1_1"><span class="lab"><font color="Green" title="E38">A6</font></span></a>, <a class="ref" href="cat_1.html#T1" onmouseover="rs('cat_1/T1')" onmouseout="rh()">CAT_1:1</a></span>;<br/><a NAME="E16:67_1_1_1"/>
 <a href="graph_1.html#K3" title="GRAPH_1:func.3">dom</a> <font color="Maroon" title="c11">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67_1_1_1"><span class="lab"><font color="Green" title="E40">A8</font></span></a>, <a class="ref" href="cat_1.html#T1" onmouseover="rs('cat_1/T1')" onmouseout="rh()">CAT_1:1</a></span>;<br/><span class="kw">hence </span><a NAME="E17:67_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67_1_1_1"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="txt" href="#E9:67_1_1_1"><span class="lab"><font color="Green" title="E37">A5</font></span></a>, <a class="txt" href="#E12:67_1_1_1"><span class="lab"><font color="Green" title="E39">A7</font></span></a>, <a class="txt" href="#E13:67_1_1_1"><span class="lab"><font color="Green" title="E40">A8</font></span></a>, <a class="txt" href="#E15:67_1_1_1"><span class="lab"><font color="Green" title="E41">A9</font></span></a>, <a class="ref" href="cat_1.html#T1" onmouseover="rs('cat_1/T1')" onmouseout="rh()">CAT_1:1</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>

<span class="kw">let </span><font color="Maroon" title="c2">o</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" title="CATALG_1:func.3">CatSign</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="msualg_6.html#D1" onmouseover="rs('msualg_6/D1')" onmouseout="rh()">MSUALG_6:def 1</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"> (  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  not  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_1_2"><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="E1:67_1_1_2"/>
( <font color="Maroon" title="c2">o</font> <a href="xfamily.html#K1" title="XFAMILY:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c2">o</font> <a href="xfamily.html#K1" title="XFAMILY:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="catalg_1.html#T16" target="_self" onmouseover="rs('catalg_1/T16')" onmouseout="rh()">Th16</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_1_1_2_1"><span class="kw">suppose </span></a><a NAME="E1:67_1_1_2_1"/>
<font color="Maroon" title="c2">o</font> <a href="xfamily.html#K1" title="XFAMILY:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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"> (  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  not  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font><span class="kw"> such that </span><br/><a NAME="E3:67_1_1_2_1"/><span class="lab"><font color="Green" title="E33">A10</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="catalg_1.html#T17" target="_self" onmouseover="rs('catalg_1/T17')" onmouseout="rh()">Th17</a></span>;<br/><a NAME="E4:67_1_1_2_1"/>
 <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c3">a</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:67_1_1_2_1"><span class="lab"><font color="Green" title="E33">A10</font></span></a>, <a class="ref" href="catalg_1.html#T26" target="_self" onmouseover="rs('catalg_1/T26')" onmouseout="rh()">Th26</a></span>;<br/><span class="kw">hence </span><a NAME="E5:67_1_1_2_1"/>
(  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  not  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T27" onmouseover="rs('cat_1/T27')" onmouseout="rh()">CAT_1:27</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="67_1_1_2_2"><span class="kw">suppose </span></a><a NAME="E1:67_1_1_2_2"/>
<font color="Maroon" title="c2">o</font> <a href="xfamily.html#K1" title="XFAMILY:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <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"> (  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  not  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font><span class="kw"> such that </span><br/><a NAME="E3:67_1_1_2_2"/><span class="lab"><font color="Green" title="E33">A11</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="catalg_1.html#T18" target="_self" onmouseover="rs('catalg_1/T18')" onmouseout="rh()">Th18</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c6">A</font> =  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>);<br/><span class="kw">assume </span><a NAME="E4:67_1_1_2_2"/><span class="lab"><font color="Green" title="E34">A12</font></span>: 
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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">  not  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><a NAME="E5:67_1_1_2_2"/>
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>)</span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:67_1_1_2_2"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="ref" href="catalg_1.html#T27" target="_self" onmouseover="rs('catalg_1/T27')" onmouseout="rh()">Th27</a></span>;<br/><a NAME="E6:67_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A13</font></span>: 
 ex <font color="Olive" title="b1">g</font>, <font color="Olive" title="b2">f</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>) &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>) &amp;  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">g</font>,<font color="Olive" title="b2">f</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67_1_1_2_2"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="ref" href="finseq_3.html#T124" onmouseover="rs('finseq_3/T124')" onmouseout="rh()">FINSEQ_3:124</a></span>;<br/><a NAME="E7:67_1_1_2_2"/>
 <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">Hom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:67_1_1_2_2"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="ref" href="catalg_1.html#T27" target="_self" onmouseover="rs('catalg_1/T27')" onmouseout="rh()">Th27</a></span>;<br/><span class="kw">hence </span><a NAME="E8:67_1_1_2_2"/>
 not  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> (<font color="Maroon" title="c2">o</font>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">C</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_1_1_2_2"><span class="lab"><font color="Green" title="E35">A13</font></span></a>, <a class="ref" href="cat_1.html#T24" onmouseover="rs('cat_1/T24')" onmouseout="rh()">CAT_1:24</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>

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