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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</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">a1</font>, <font color="Olive" title="b2">a2</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">b2</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> holds <br/> ( (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</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_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">b2</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>  ) iff  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Olive" title="b1">a1</font>,<font color="Olive" title="b3">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Olive" title="b2">a2</font>,<font color="Olive" title="b4">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></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>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c4">a2</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"> for <font color="Olive" title="b1">b1</font>, <font color="Olive" title="b2">b2</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> holds <br/> ( (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</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_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Olive" title="b1">b1</font>,<font color="Olive" title="b2">b2</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>  ) iff  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Olive" title="b1">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c4">a2</font>,<font color="Olive" title="b2">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></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>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">b1</font>, <font color="Maroon" title="c6">b2</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</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_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</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>  ) iff  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></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>  )</span><br/>







<a NAME="E1:15"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</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">a1</font>,<font color="Maroon" title="c4">a2</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="c5">b1</font>,<font color="Maroon" title="c6">b2</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T42" title="CAT_2:th.42">CAT_2:42</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:15"/>
( (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</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_1.html#K3" title="CAT_1:func.3">Hom</a> <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</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>  ) iff  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></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>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T113" title="ZFMISC_1:th.113">ZFMISC_1:113</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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