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<span class="kw">let </span><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> ; <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">M</font> being   <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>  st <font color="Olive" title="b1">M</font> is  <a href="functor0.html#V11" title="FUNCTOR0:attr.11">Contravariant</a>  &amp; <font color="Olive" title="b1">M</font> is  <a href="functor0.html#V5" title="FUNCTOR0:attr.5">onto</a>  holds <br/><font color="Olive" title="b1">M</font> is  <a href="functor0.html#V7" title="FUNCTOR0:attr.7">coreflexive</a> </span><br/><span class="kw">let </span><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>; <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="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>  implies <font color="Maroon" title="c3">M</font> is  <a href="functor0.html#V7" title="FUNCTOR0:attr.7">coreflexive</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:117"/><span class="lab"><font color="Green" title="E77">A1</font></span>: 
( <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>  )
 ; <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="c3">M</font> is  <a href="functor0.html#V7" title="FUNCTOR0:attr.7">coreflexive</a> </span><br/>

<a NAME="E2:117"/><span class="kw">then </span>
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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D14" target="_self" title="FUNCTOR0:def.14">Def14</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E4:117"/><span class="lab"><font color="Green" title="E78">A2</font></span>: 
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">M</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#D3" target="_self" title="FUNCTOR0:def.3">Def3</a></span>;<br/>
<a NAME="E5:117"/>
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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:117"><span class="lab"><font color="Green" title="E77">A1</font></span></a>, <a class="ref" href="functor0.html#D8" target="_self" title="FUNCTOR0:def.8">Def8</a></span>;<br/>
<a NAME="E6:117"/><span class="kw">then </span>
<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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:117"><span class="lab"><font color="Green" title="E78">A2</font></span></a>, <a class="ref" href="functor0.html#T14" target="_self" title="FUNCTOR0:th.14">Th14</a></span>;<br/>
<a NAME="E7:117"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A3</font></span>: 
<font color="Maroon" title="c4">f</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="functor0.html#T5" target="_self" title="FUNCTOR0:th.5">Th5</a></span>;<br/>
<a NAME="E8:117"/>
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#K7" title="RELSET_1:func.7">.:</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="relset_1.html#R2" title="RELSET_1:pred.2">=</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#K7" title="RELSET_1:func.7">.:</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:117"><span class="lab"><font color="Green" title="E78">A2</font></span></a>, <a class="ref" href="functor0.html#T4" target="_self" title="FUNCTOR0:th.4">Th4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:117"/>
 <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="relset_1.html#R1" title="RELSET_1: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#K7" title="RELSET_1:func.7">.:</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:117"><span class="lab"><font color="Green" title="E79">A3</font></span></a>, <a class="ref" href="functor0.html#T12" target="_self" title="FUNCTOR0:th.12">Th12</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="functor0.html#D10" target="_self" title="FUNCTOR0:def.10">FUNCTOR0:def 10</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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