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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="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font><br/>  for <font color="Olive" title="b2">a</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C1</font> holds  <span class="p1">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="cat_1.html#K8" title="CAT_1:func.8">.</a> <font color="Olive" title="b2">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C1</font> holds  <span class="p1">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K8" title="CAT_1:func.8">.</a> <font color="Olive" title="b1">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K8" title="CAT_1:func.8">.</a> <font color="Maroon" title="c4">a</font></span>)</span></span><br/>





<a NAME="E1:58"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E2:58"/>
( <span class="p1">(<span class="default"><a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="xfamily.html#K1" title="XFAMILY:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <span class="p1">(<span class="default"><a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">a</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )
 
;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="catalg_1.html#K12" title="CATALG_1:func.12">Psi</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <font color="Maroon" title="c4">a</font></span>)</span> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">a</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></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="catalg_1.html#D12" target="_self" onmouseover="rs('catalg_1/D12')" onmouseout="rh()">Def12</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="txt" href="catalg_1.html#E36"><span class="lab"><font color="Green" title="E23">Lm4</font></span></a></span>
<br/>.= 
 <a href="catalg_1.html#K8" title="CATALG_1:func.8">idsym</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K8" title="CAT_1:func.8">.</a> <font color="Maroon" title="c4">a</font></span>)</span>

;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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