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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="functor0.html#L2">FunctorStr</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>



<b>assume </b><a NAME="E1:9"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="functor0.html#V21">bijective</a>
 ;<br/>

<a NAME="E2:9"/><b>then </b><i><font color="Green">E5</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="functor0.html#V19">injective</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D36">FUNCTOR0:def 36</a></i>;<br/>
<a NAME="E3:9"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is <a href="functor0.html#V4">one-to-one</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D34">FUNCTOR0:def 34</a></i>;<br/>
<a NAME="E4:9"/><b>then </b><i><font color="Green">E6</font></i>: 
the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D7">FUNCTOR0:def 7</a></i>;<br/>
<a NAME="E5:9"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="functor0.html#V17">faithful</a>
 
<b>by </b><i><a class="txt" href="functor1.html#E2:9"><i><font color="Green">E5</font></i></a>, <a class="ref" href="functor0.html#D34">FUNCTOR0:def 34</a></i>;<br/>
<a NAME="E6:9"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="functor0.html#V20">surjective</a>
 
<b>by </b><i><a class="txt" href="functor1.html#E1:9"><i><font color="Green">E4</font></i></a>, <a class="ref" href="functor0.html#D36">FUNCTOR0:def 36</a></i>;<br/>
<a NAME="E7:9"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is <a href="functor0.html#V5">onto</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D35">FUNCTOR0:def 35</a></i>;<br/>
<a NAME="E8:9"/><b>then </b>
the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D8">FUNCTOR0:def 8</a></i>;<br/>
<b>hence </b><a NAME="E9:9"/>
( the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">c<sub>3</sub></font> is <a href="funct_2.html#V3">bijective</a> &amp; the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>3</sub></font> is <a href="msualg_3.html#V1">"1-1"</a> )
 <b>by </b><i><a class="txt" href="functor1.html#E4:9"><i><font color="Green">E6</font></i></a>, <a class="txt" href="functor1.html#E5:9"><i><font color="Green">E7</font></i></a>, <a class="ref" href="functor0.html#D31">FUNCTOR0:def 31</a>, <a class="ref" href="funct_2.html#D4">FUNCT_2:def 4</a></i>;<br/>


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