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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="Red">::  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#V4" title="FUNCTOR0:attr.4">one-to-one</a>  &amp; <font color="Olive" title="b4">G</font> is  <a href="functor0.html#V4" title="FUNCTOR0:attr.4">one-to-one</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#V4" title="FUNCTOR0:attr.4">one-to-one</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="Red">::  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#V4" title="FUNCTOR0:attr.4">one-to-one</a>  &amp; <font color="Olive" title="b2">G</font> is  <a href="functor0.html#V4" title="FUNCTOR0:attr.4">one-to-one</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#V4" title="FUNCTOR0:attr.4">one-to-one</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="Red">::  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#V4" title="FUNCTOR0:attr.4">one-to-one</a>  &amp; <font color="Olive" title="b1">G</font> is  <a href="functor0.html#V4" title="FUNCTOR0:attr.4">one-to-one</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#V4" title="FUNCTOR0:attr.4">one-to-one</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="Red">::  thesis: </font></span></a><span class="hide"> ( <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>  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#V4" title="FUNCTOR0:attr.4">one-to-one</a>  )</span><br/>







<span class="kw">assume </span><a NAME="E1:10"/>
( <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>  )
 ; <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="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><br/>

<a NAME="E2:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A1</font></span>: 
( the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">F</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">G</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D7" title="FUNCTOR0:def.7">FUNCTOR0:def 7</a></span>;<br/>
<a NAME="E3:10"/>
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D37" title="FUNCTOR0:def.37">FUNCTOR0:def 37</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:10"/>
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c4">F</font></span>)</span> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E5">A1</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="functor0.html#D7" title="FUNCTOR0:def.7">FUNCTOR0:def 7</a> <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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