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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</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">I</font> being  <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c1">C</font><br/> for <font color="Olive" title="b2">T</font> being   <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Olive" title="b1">I</font> holds   <a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Olive" title="b2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font> be   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c1">C</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">T</font> being   <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Maroon" title="c2">I</font> holds   <a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">T</font> be    <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Maroon" title="c2">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span><br/>





<a NAME="E1:60"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E27">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> implies <span class="p1">(<span class="default"><a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:60_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">f</font> = <font color="Maroon" title="c4">x</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> ;<br/><a NAME="E3:60_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <span class="p4">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c5">f</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K8" title="INDEX_1:func.8">`1</a> </span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <span class="p4">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c5">f</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c5">f</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="index_1.html#D11" target="_self" title="INDEX_1:def.11">Def11</a></span>;<br/><a NAME="E4:60_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="index_1.html#K11" title="INDEX_1:func.11">.</a> <font color="Maroon" title="c5">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><span class="kw">hence </span><a NAME="E5:60_1"/>
<span class="p1">(<span class="default"><a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="mcart_1.html#D13" title="MCART_1:def.13">MCART_1:def 13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E3:60"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">C</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#D13" title="MCART_1:def.13">MCART_1:def 13</a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:60"/>
 <a href="mcart_1.html#K16" title="MCART_1:func.16">pr2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="index_1.html#K13" title="INDEX_1:func.13">-functor</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I</font> <a href="index_1.html#K12" title="INDEX_1:func.12">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></span>; <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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