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<span class="kw">consider </span><font color="Maroon" title="c4">d</font> being   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c5">p1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c2">c1</font>, <font color="Maroon" title="c6">p2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c3">c2</font><span class="kw"> such that </span><br/><a NAME="E2:62_1_1"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
(  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c2">c1</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c3">c2</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font> <a href="cat_8.html#R1" title="CAT_8:pred.1">is_product_of</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c3">c2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_8.html#D11" target="_self" onmouseover="rs('cat_8/D11')" onmouseout="rh()">Def11</a></span>;<br/>
<span class="kw">take </span>
<span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.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">  ex <font color="Olive" title="b1">d</font> being   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b2">p1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c2">c1</font> ex <font color="Olive" title="b3">p2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c3">c2</font> st <br/>( <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Olive" title="b1">d</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b1">d</font>,<font color="Maroon" title="c2">c1</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b1">d</font>,<font color="Maroon" title="c3">c2</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">d</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> <a href="cat_8.html#R1" title="CAT_8:pred.1">is_product_of</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c3">c2</font> )</span><br/>

<span class="kw">thus </span><a NAME="E3:62_1_1"/>
 ex <font color="Olive" title="b1">d</font> being   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b2">p1</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c2">c1</font> ex <font color="Olive" title="b3">p2</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b1">d</font>,<font color="Maroon" title="c3">c2</font> st <br/>( <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c5">p1</font>,<font color="Maroon" title="c6">p2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Olive" title="b1">d</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b1">d</font>,<font color="Maroon" title="c2">c1</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_7.html#K1" title="CAT_7:func.1">Hom</a> (<font color="Olive" title="b1">d</font>,<font color="Maroon" title="c3">c2</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">d</font>,<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> <a href="cat_8.html#R1" title="CAT_8:pred.1">is_product_of</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c3">c2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:62_1_1"><span class="lab"><font color="Green" title="E33">A1</font></span></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/>


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