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<span class="kw">let </span><font color="Maroon" title="c1">C1</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</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">C2</font>, <font color="Olive" title="b2">C3</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>   <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</a> <br/>  for <font color="Olive" title="b3">F</font> being   <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">C1</font>,<font color="Olive" title="b1">C2</font><br/>  for <font color="Olive" title="b4">G</font> being    <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Olive" title="b1">C2</font>,<font color="Olive" title="b2">C3</font>  st <font color="Olive" title="b3">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>  &amp; <font color="Olive" title="b4">G</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>  holds <br/><font color="Olive" title="b4">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b3">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">C2</font>, <font color="Maroon" title="c3">C3</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>   <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</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">F</font> being   <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font><br/>  for <font color="Olive" title="b2">G</font> being    <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c3">C3</font>  st <font color="Olive" title="b1">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>  &amp; <font color="Olive" title="b2">G</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>  holds <br/><font color="Olive" title="b2">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b1">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>; <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">G</font> being    <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c3">C3</font>  st <font color="Maroon" title="c4">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>  &amp; <font color="Olive" title="b1">G</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>  holds <br/><font color="Olive" title="b1">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">G</font> be    <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c3">C3</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="c4">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>  &amp; <font color="Maroon" title="c5">G</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>  implies <font color="Maroon" title="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>  )</span><br/>







<span class="kw">assume </span><a NAME="E1:14"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
( <font color="Maroon" title="c4">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>  &amp; <font color="Maroon" title="c5">G</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>  )
 ; <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="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a> </span><br/>

<a NAME="E2:14"/><span class="kw">then </span>
( <font color="Maroon" title="c4">F</font> is  <a href="functor0.html#V17" title="FUNCTOR0:attr.17">faithful</a>  &amp; <font color="Maroon" title="c5">G</font> is  <a href="functor0.html#V17" title="FUNCTOR0:attr.17">faithful</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D33" title="FUNCTOR0:def.33">FUNCTOR0:def 33</a></span>;<br/>
<a NAME="E3:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A2</font></span>: 
<font color="Maroon" title="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is  <a href="functor0.html#V17" title="FUNCTOR0:attr.17">faithful</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor1.html#T7" target="_self" title="FUNCTOR1:th.7">Th8</a></span>;<br/>
<a NAME="E4:14"/>
( <font color="Maroon" title="c4">F</font> is  <a href="functor0.html#V4" title="FUNCTOR0:attr.4">one-to-one</a>  &amp; <font color="Maroon" title="c5">G</font> is  <a href="functor0.html#V4" title="FUNCTOR0:attr.4">one-to-one</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="functor0.html#D33" title="FUNCTOR0:def.33">FUNCTOR0:def 33</a></span>;<br/>
<a NAME="E5:14"/><span class="kw">then </span>
<font color="Maroon" title="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is  <a href="functor0.html#V4" title="FUNCTOR0:attr.4">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor1.html#T6" target="_self" title="FUNCTOR1:th.6">Th7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14"/>
<font color="Maroon" title="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font> is  <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="functor0.html#D33" title="FUNCTOR0:def.33">FUNCTOR0:def 33</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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