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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>  st  <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>  holds <br/>for <font color="Olive" title="b5">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b6">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font> holds <br/> ( <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b5">f</font>,<font color="Olive" title="b6">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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> iff ( <font color="Olive" title="b5">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</font> &amp; <font color="Olive" title="b6">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">b2</font> ) )</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>  st  <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>  holds <br/>for <font color="Olive" title="b3">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b4">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font> holds <br/> ( <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b3">f</font>,<font color="Olive" title="b4">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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> iff ( <font color="Olive" title="b3">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Olive" title="b4">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">b1</font>,<font color="Olive" title="b2">b2</font> ) )</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> <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>  implies for <font color="Olive" title="b1">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b2">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font> holds <br/> ( <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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> iff ( <font color="Olive" title="b1">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Olive" title="b2">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> ) ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:16"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
 <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> 
 ; <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">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b2">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font> holds <br/> ( <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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> iff ( <font color="Olive" title="b1">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Olive" title="b2">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> ) )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</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">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font> holds <br/> ( <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c7">f</font>,<font color="Olive" title="b1">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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> iff ( <font color="Maroon" title="c7">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Olive" title="b1">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">g</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</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"> ( <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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> iff ( <font color="Maroon" title="c7">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c8">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> ) )</span><br/>



<span class="kw">thus </span><a NAME="E2:16"/>
( <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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> implies ( <font color="Maroon" title="c7">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c8">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> ) )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c8">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> implies <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:16_1"/>
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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 class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c8">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> )</span><br/>

<a NAME="E2:16_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="cat_1.html#D7" title="CAT_1:def.7">CAT_1:def 7</a></span>;<br/>
<a NAME="E3:16_1"/>
 <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/>
<a NAME="E4:16_1"/><span class="kw">then </span>
( <font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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> &amp; <font color="Maroon" title="c8">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:16_1"/>
( <font color="Maroon" title="c7">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c8">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#D7" title="CAT_1:def.7">CAT_1:def 7</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/>


</div><span class="kw">end;</span></div>

<a NAME="E3:16"/>
(  <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="isocat_2.html#T13" target="_self" title="ISOCAT_2:th.13">Th13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:16"/>
( <font color="Maroon" title="c7">f</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c8">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c5">b1</font>,<font color="Maroon" title="c6">b2</font> implies <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T43" title="CAT_2:th.43">CAT_2:43</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/>


</div>
