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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds <br/> (  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">A</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#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> &amp;  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">A</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#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> &amp;  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> )</span><br/>



<a NAME="E1:72"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> holds  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">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="catalg_1.html#D15" target="_self" title="CATALG_1:def.15">Def15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:72"/>
(  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">A</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#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> &amp;  <a href="msualg_1.html#K4" title="MSUALG_1:func.4">Result</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" title="CATALG_1:func.10">compsym</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" title="CATALG_1:func.13">MSAlg</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="catalg_1.html#E51"><span class="lab"><font color="Green" title="E27">Lm3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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