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<b>let </b><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font> be    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ;<br/><b>let </b><font color="Maroon" title="c3">M</font> be    <a href="functor0.html#L1" title="FUNCTOR0:struct.1">BimapStr</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>;<br/>



<b>assume </b><a NAME="E1:116"/><i><font color="Green" title="E77">A1</font></i>: 
( <font color="Maroon" title="c3">M</font> is <a href="functor0.html#V11" title="FUNCTOR0:attr.11">Contravariant</a> &amp; <font color="Maroon" title="c3">M</font> is <a href="functor0.html#V5" title="FUNCTOR0:attr.5">onto</a> )
 ;<br/>

<a NAME="E2:116"/><b>then </b>
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">M</font> is <a href="functor0.html#V2" title="FUNCTOR0:attr.2">Contravariant</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D14" target="_self" title="FUNCTOR0:def.14">Def14</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font><b> such that </b><br/><a NAME="E4:116"/><i><font color="Green" title="E78">A2</font></i>: 
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="functor0.html#K1" title="FUNCTOR0:func.1">~</a> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c4">f</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span>
 <b>by </b><i><a class="ref" href="functor0.html#D3" target="_self" title="FUNCTOR0:def.3">Def3</a></i>;<br/>
<a NAME="E5:116"/>
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">M</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>
 
<b>by </b><i><a class="txt" href="functor0.html#E1:116"><i><font color="Green" title="E77">A1</font></i></a>, <a class="ref" href="functor0.html#D8" target="_self" title="FUNCTOR0:def.8">Def8</a></i>;<br/>
<a NAME="E6:116"/><b>then </b>
<span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c4">f</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>
 
<b>by </b><i><a class="txt" href="functor0.html#E4:116"><i><font color="Green" title="E78">A2</font></i></a>, <a class="ref" href="functor0.html#T14" target="_self" title="FUNCTOR0:th.14">Th14</a></i>;<br/>
<a NAME="E7:116"/><b>then </b><i><font color="Green" title="E79">A3</font></i>: 
<font color="Maroon" title="c4">f</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>
 
<b>by </b><i><a class="ref" href="functor0.html#T5" target="_self" title="FUNCTOR0:th.5">Th5</a></i>;<br/>
<a NAME="E8:116"/>
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">M</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c4">f</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="functor0.html#E4:116"><i><font color="Green" title="E78">A2</font></i></a>, <a class="ref" href="functor0.html#T4" target="_self" title="FUNCTOR0:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E9:116"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">M</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font></span>)</span>
 <b>by </b><i><a class="txt" href="functor0.html#E7:116"><i><font color="Green" title="E79">A3</font></i></a>, <a class="ref" href="functor0.html#T12" target="_self" title="FUNCTOR0:th.12">Th12</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D10" target="_self" title="FUNCTOR0:def.10">FUNCTOR0:def 10</a><br/>


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