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<span class="kw">let </span><font color="Maroon" title="c1">o</font>, <font color="Maroon" title="c2">m</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>) is  <a href="cat_4.html#V3" title="CAT_4:attr.3">Cartesian</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">1PCat</font> =  <a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>);<br/>
<span class="kw">thus </span><a NAME="E1:19"/>
 the <a href="cat_4.html#U1" title="CAT_4:sel.1">TerminalObj</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_4.html#T8" target="_self" title="CAT_4:th.8">Th10</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_4.html#D8" target="_self" title="CAT_4:def.8">CAT_4:def 8</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">a</font>, <font color="Olive" title="b2">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> holds <br/> (  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"> the <a href="cat_4.html#U3" title="CAT_4:sel.3">Proj1</a> of <span class="p2">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</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> <font color="Olive" title="b1">a</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"> the <a href="cat_4.html#U4" title="CAT_4:sel.4">Proj2</a> of <span class="p2">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</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> <font color="Olive" title="b2">b</font> &amp;  the <a href="cat_4.html#U2" title="CAT_4:sel.2">CatProd</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a>  the <a href="cat_4.html#U3" title="CAT_4:sel.3">Proj1</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>), the <a href="cat_4.html#U4" title="CAT_4:sel.4">Proj2</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"> the <a href="cat_4.html#U3" title="CAT_4:sel.3">Proj1</a> of <span class="p2">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"> the <a href="cat_4.html#U4" title="CAT_4:sel.4">Proj2</a> of <span class="p2">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> &amp;  the <a href="cat_4.html#U2" title="CAT_4:sel.2">CatProd</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>) <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a>  the <a href="cat_4.html#U3" title="CAT_4:sel.3">Proj1</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>), the <a href="cat_4.html#U4" title="CAT_4:sel.4">Proj2</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>) )</span><br/>

<span class="kw">thus </span><a NAME="E2:19"/>
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"> the <a href="cat_4.html#U3" title="CAT_4:sel.3">Proj1</a> of <span class="p2">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_4.html#T3" target="_self" title="CAT_4:th.3">Th4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"> the <a href="cat_4.html#U4" title="CAT_4:sel.4">Proj2</a> of <span class="p2">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> &amp;  the <a href="cat_4.html#U2" title="CAT_4:sel.2">CatProd</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>) <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a>  the <a href="cat_4.html#U3" title="CAT_4:sel.3">Proj1</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>), the <a href="cat_4.html#U4" title="CAT_4:sel.4">Proj2</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>) )</span><br/>

<span class="kw">thus </span><a NAME="E3:19"/>
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"> the <a href="cat_4.html#U4" title="CAT_4:sel.4">Proj2</a> of <span class="p2">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_4.html#T3" target="_self" title="CAT_4:th.3">Th4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="cat_4.html#U2" title="CAT_4:sel.2">CatProd</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>) <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a>  the <a href="cat_4.html#U3" title="CAT_4:sel.3">Proj1</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>), the <a href="cat_4.html#U4" title="CAT_4:sel.4">Proj2</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)</span><br/>

<span class="kw">thus </span><a NAME="E4:19"/>
 the <a href="cat_4.html#U2" title="CAT_4:sel.2">CatProd</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>) <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a>  the <a href="cat_4.html#U3" title="CAT_4:sel.3">Proj1</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>), the <a href="cat_4.html#U4" title="CAT_4:sel.4">Proj2</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" title="CAT_4:func.5">c1Cat</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_4.html#T9" target="_self" title="CAT_4:th.9">Th11</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/>


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