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<span class="kw">let </span><font color="Maroon" title="c1">I</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">C</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/>  for <font color="Olive" title="b2">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">I</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span><br/>  for <font color="Olive" title="b3">c</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span> holds <br/> ( <font color="Olive" title="b2">F</font> is    <a href="cat_3.html#M2" title="CAT_3:mode.2">Injections_family</a> of <font color="Olive" title="b3">c</font>,<font color="Maroon" title="c1">I</font> iff  <a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Olive" title="b2">F</font> is    <a href="cat_3.html#M1" title="CAT_3:mode.1">Projections_family</a> of  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Olive" title="b3">c</font>,<font color="Maroon" title="c1">I</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">I</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span><br/>  for <font color="Olive" title="b2">c</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span> holds <br/> ( <font color="Olive" title="b1">F</font> is    <a href="cat_3.html#M2" title="CAT_3:mode.2">Injections_family</a> of <font color="Olive" title="b2">c</font>,<font color="Maroon" title="c1">I</font> iff  <a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Olive" title="b1">F</font> is    <a href="cat_3.html#M1" title="CAT_3:mode.1">Projections_family</a> of  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Olive" title="b2">c</font>,<font color="Maroon" title="c1">I</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">I</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">c</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span> holds <br/> ( <font color="Maroon" title="c3">F</font> is    <a href="cat_3.html#M2" title="CAT_3:mode.2">Injections_family</a> of <font color="Olive" title="b1">c</font>,<font color="Maroon" title="c1">I</font> iff  <a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font> is    <a href="cat_3.html#M1" title="CAT_3:mode.1">Projections_family</a> of  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Olive" title="b1">c</font>,<font color="Maroon" title="c1">I</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">c</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">F</font> is    <a href="cat_3.html#M2" title="CAT_3:mode.2">Injections_family</a> of <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c1">I</font> iff  <a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font> is    <a href="cat_3.html#M1" title="CAT_3:mode.1">Projections_family</a> of  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c1">I</font> )</span><br/>







<span class="kw">thus </span><a NAME="E1:84"/>
( <font color="Maroon" title="c3">F</font> is    <a href="cat_3.html#M2" title="CAT_3:mode.2">Injections_family</a> of <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c1">I</font> implies  <a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font> is    <a href="cat_3.html#M1" title="CAT_3:mode.1">Projections_family</a> of  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c1">I</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font> is    <a href="cat_3.html#M1" title="CAT_3:mode.1">Projections_family</a> of  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c1">I</font> implies <font color="Maroon" title="c3">F</font> is    <a href="cat_3.html#M2" title="CAT_3:mode.2">Injections_family</a> of <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c1">I</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:84_1"/><span class="lab"><font color="Green" title="E49">A1</font></span>: 
 <a href="cat_3.html#K3" title="CAT_3:func.3">cods</a> <font color="Maroon" title="c3">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c4">c</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_3.html#D15" target="_self" title="CAT_3:def.15">CAT_3:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font> is    <a href="cat_3.html#M1" title="CAT_3:mode.1">Projections_family</a> of  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c1">I</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> implies <span class="p1">(<span class="default"><a href="cat_3.html#K2" title="CAT_3:func.2">doms</a> <span class="p2">(<span class="default"><a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:84_1_1"/><span class="lab"><font color="Green" title="E50">A2</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" 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="cat_3.html#K2" title="CAT_3:func.2">doms</a> <span class="p2">(<span class="default"><a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span><br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="cat_3.html#K2" title="CAT_3:func.2">doms</a> <span class="p2">(<span class="default"><a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font> = 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_3.html#D1" target="_self" title="CAT_3:def.1">Def3</a></span>
<br/>.= 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_1_1"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="cat_3.html#D4" target="_self" title="CAT_3:def.4">Def6</a></span>
<br/>.= 
 <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="oppcat_1.html#T11" title="OPPCAT_1:th.11">OPPCAT_1:11</a></span>
<br/>.= 
 <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_1"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="txt" href="#E1:84_1_1"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="cat_3.html#D2" target="_self" title="CAT_3:def.2">Def4</a></span>
<br/>.= 
 <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_1_1"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="cat_3.html#T2" target="_self" title="CAT_3:th.2">Th2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_1_1"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="cat_3.html#T2" target="_self" title="CAT_3:th.2">Th2</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:84_1"/>
 <a href="cat_3.html#K2" title="CAT_3:func.2">doms</a> <span class="p1">(<span class="default"><a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_3.html#T1" target="_self" title="CAT_3:th.1">Th1</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_3.html#D12" target="_self" title="CAT_3:def.12">CAT_3:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:84"/><span class="lab"><font color="Green" title="E49">A3</font></span>: 
 <a href="cat_3.html#K2" title="CAT_3:func.2">doms</a> <span class="p1">(<span class="default"><a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font></span>)</span>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_3.html#D12" target="_self" title="CAT_3:def.12">CAT_3:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">F</font> is    <a href="cat_3.html#M2" title="CAT_3:mode.2">Injections_family</a> of <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c1">I</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> implies <span class="p1">(<span class="default"><a href="cat_3.html#K3" title="CAT_3:func.3">cods</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:84_2"/><span class="lab"><font color="Green" title="E50">A4</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" 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="cat_3.html#K3" title="CAT_3:func.3">cods</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span><br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="cat_3.html#K3" title="CAT_3:func.3">cods</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font> = 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_3.html#D2" target="_self" title="CAT_3:def.2">Def4</a></span>
<br/>.= 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="oppcat_1.html#T9" title="OPPCAT_1:th.9">OPPCAT_1:9</a></span>
<br/>.= 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_3.html#K5" title="CAT_3:func.5">opp</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_2"><span class="lab"><font color="Green" title="E50">A4</font></span></a>, <a class="ref" href="cat_3.html#D4" target="_self" title="CAT_3:def.4">Def6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:84"><span class="lab"><font color="Green" title="E49">A3</font></span></a>, <a class="txt" href="#E1:84_2"><span class="lab"><font color="Green" title="E50">A4</font></span></a>, <a class="ref" href="cat_3.html#D1" target="_self" title="CAT_3:def.1">Def3</a></span>
<br/>.= 
 <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c4">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_2"><span class="lab"><font color="Green" title="E50">A4</font></span></a>, <a class="ref" href="cat_3.html#T2" target="_self" title="CAT_3:th.2">Th2</a></span>
<br/>.= 
<font color="Maroon" title="c4">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="oppcat_1.html#D3" title="OPPCAT_1:def.3">OPPCAT_1:def 3</a></span>
<br/>.= 
<font color="Maroon" title="c4">c</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="oppcat_1.html#D2" title="OPPCAT_1:def.2">OPPCAT_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_2"><span class="lab"><font color="Green" title="E50">A4</font></span></a>, <a class="ref" href="cat_3.html#T2" target="_self" title="CAT_3:th.2">Th2</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:84"/>
 <a href="cat_3.html#K3" title="CAT_3:func.3">cods</a> <font color="Maroon" title="c3">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_3.html#T1" target="_self" title="CAT_3:th.1">Th1</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_3.html#D15" target="_self" title="CAT_3:def.15">CAT_3:def 15</a> <a class="txt" 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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