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<a NAME="E1:93_1_2"/><span class="lab"><font color="Green" title="E44">A4</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c3">b</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c3">b</font></span>)</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="cat_4.html#T62" target="_self" title="CAT_4:th.62">Th66</a></span>;<br/>
<a NAME="E2:93_1_2"/>
( <font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c3">b</font> <a href="cat_3.html#R4" title="CAT_3:pred.4">is_a_coproduct_wrt</a>  <a href="cat_4.html#K25" title="CAT_4:func.25">in1</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>), <a href="cat_4.html#K26" title="CAT_4:func.26">in2</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>) &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c3">b</font></span>)</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="cat_4.html#D26" target="_self" title="CAT_4:def.26">Def27</a>, <a class="ref" href="cat_4.html#T62" target="_self" title="CAT_4:th.62">Th66</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">h</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font><span class="kw"> such that </span><br/><a NAME="E4:93_1_2"/><span class="lab"><font color="Green" title="E45">A5</font></span>: 
 for <font color="Olive" title="b1">k</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> holds <br/> ( ( <font color="Olive" title="b1">k</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K25" title="CAT_4:func.25">in1</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> &amp; <font color="Olive" title="b1">k</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K26" title="CAT_4:func.26">in2</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font> ) iff <font color="Maroon" title="c7">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:93"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E1:93_1_2"><span class="lab"><font color="Green" title="E44">A4</font></span></a>, <a class="ref" href="cat_3.html#T81" title="CAT_3:th.81">CAT_3:81</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c8">h1</font>, <font color="Maroon" title="c9">h2</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">h1</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K25" title="CAT_4:func.25">in1</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> &amp; <font color="Maroon" title="c8">h1</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K26" title="CAT_4:func.26">in2</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font> &amp; <font color="Maroon" title="c9">h2</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K25" title="CAT_4:func.25">in1</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> &amp; <font color="Maroon" title="c9">h2</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K26" title="CAT_4:func.26">in2</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font> implies <font color="Maroon" title="c8">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">h2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E5:93_1_2"/><span class="lab"><font color="Green" title="E46">A6</font></span>: 
( <font color="Maroon" title="c8">h1</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K25" title="CAT_4:func.25">in1</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> &amp; <font color="Maroon" title="c8">h1</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K26" title="CAT_4:func.26">in2</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font> )
 <span class="kw">and </span><br/><a NAME="E6:93_1_2"/><span class="lab"><font color="Green" title="E47">A7</font></span>: 
( <font color="Maroon" title="c9">h2</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K25" title="CAT_4:func.25">in1</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> &amp; <font color="Maroon" title="c9">h2</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K26" title="CAT_4:func.26">in2</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">h2</font></span><br/>

<a NAME="E7:93_1_2"/>
<font color="Maroon" title="c8">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:93_1_2"><span class="lab"><font color="Green" title="E46">A6</font></span></a>, <a class="txt" href="#E4:93_1_2"><span class="lab"><font color="Green" title="E45">A5</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:93_1_2"/>
<font color="Maroon" title="c8">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">h2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:93_1_2"><span class="lab"><font color="Green" title="E47">A7</font></span></a>, <a class="txt" href="#E4:93_1_2"><span class="lab"><font color="Green" title="E45">A5</font></span></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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