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<b>let </b><font color="Maroon">C1</font> be    <a href="struct_0.html#L1">1-sorted</a> , <font color="Maroon">C2</font> be    <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">M</font> be    <a href="functor0.html#L1" target="_self">BimapStr</a> of <font color="Maroon">C1</font>,<font color="Maroon">C2</font>;<br/>



<b>assume </b><a NAME="E1:116"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">M</font> is <a href="functor0.html#V11" target="_self">Contravariant</a> &amp; <font color="Maroon">M</font> is <a href="functor0.html#V5" target="_self">onto</a> )
 ;<br/>

<a NAME="E2:116"/><b>then </b>
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">M</font> is <a href="functor0.html#V2" target="_self">Contravariant</a>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C2</font><b> such that </b><br/><a NAME="E4:116"/><i><font color="Green">E23</font></i>: 
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">M</font> <a href="hidden.html#R1">=</a>  <a href="functor0.html#K1" target="_self">~</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">f</font></span><a href="funct_3.html#K16">:]</a></span>
 <b>by </b><i/>;<br/>
<a NAME="E5:116"/>
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">M</font> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:116"/><b>then </b>
<span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">f</font></span><a href="funct_3.html#K16">:]</a></span> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:116"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">f</font> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i/>;<br/>
<a NAME="E8:116"/>
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">M</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">f</font></span><a href="funct_3.html#K16">:]</a></span> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C1</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E9:116"/>
 <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C2</font> <a href="tarski.html#R1">c=</a> the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">M</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C1</font></span>)</span>
 <b>by </b><i>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D10" target="_self">FUNCTOR0:def 10</a><br/>


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