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<b>let </b><font color="Maroon" title="c1">C1</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C2</font>, <font color="Olive" title="b2">C3</font>, <font color="Olive" title="b3">C4</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>  <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</a> <br/> for <font color="Olive" title="b4">F</font> being <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">C1</font>,<font color="Olive" title="b1">C2</font><br/> for <font color="Olive" title="b5">G</font> being <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Olive" title="b1">C2</font>,<font color="Olive" title="b2">C3</font><br/> for <font color="Olive" title="b6">H</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Olive" title="b2">C3</font>,<font color="Olive" title="b3">C4</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b6">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b5">G</font></span>)</span> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b4">F</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">C2</font>, <font color="Maroon" title="c3">C3</font>, <font color="Maroon" title="c4">C4</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#V1" title="ALTCAT_2:attr.1">reflexive</a>  <a href="altcat_1.html#L1" title="ALTCAT_1:struct.1">AltGraph</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font> being <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font><br/> for <font color="Olive" title="b2">G</font> being <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c3">C3</font><br/> for <font color="Olive" title="b3">H</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c3">C3</font>,<font color="Maroon" title="c4">C4</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b2">G</font></span>)</span> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b1">F</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">F</font> be  <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G</font> being <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c3">C3</font><br/> for <font color="Olive" title="b2">H</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c3">C3</font>,<font color="Maroon" title="c4">C4</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">G</font> be  <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a>  <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c2">C2</font>,<font color="Maroon" title="c3">C3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">H</font> being   <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c3">C3</font>,<font color="Maroon" title="c4">C4</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c7">H</font> be    <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c3">C3</font>,<font color="Maroon" title="c4">C4</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c7">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span></span><br/>









<i><font color="Green" title="E63">A1</font></i>: the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span> = 
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c7">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font>
<b>by </b><i><a class="ref" href="functor0.html#D37" target="_self" title="FUNCTOR0:def.37">Def37</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c7">H</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c6">G</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font>
<b>by </b><i><a class="ref" href="functor0.html#D37" target="_self" title="FUNCTOR0:def.37">Def37</a></i>
<br/>.= 
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c7">H</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default">the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c6">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
<br/>.= 
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c7">H</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#D37" target="_self" title="FUNCTOR0:def.37">Def37</a></i>
<br/>.= 
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c7">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#D37" target="_self" title="FUNCTOR0:def.37">Def37</a></i>
;<br/>
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span> = 
<span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c7">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c5">F</font>
<b>by </b><i><a class="ref" href="functor0.html#D37" target="_self" title="FUNCTOR0:def.37">Def37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c7">H</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c6">G</font></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">G</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c5">F</font>
<b>by </b><i><a class="ref" href="functor0.html#D37" target="_self" title="FUNCTOR0:def.37">Def37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c7">H</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c6">G</font></span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> <span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">G</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c5">F</font>
<b>by </b><i><a class="ref" href="functor0.html#T13" target="_self" title="FUNCTOR0:th.13">Th13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c7">H</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <span class="p3">(<span class="default">the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c6">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> <span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">G</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c5">F</font>
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c7">H</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> <span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">G</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c5">F</font>
<b>by </b><i><a class="ref" href="functor0.html#D37" target="_self" title="FUNCTOR0:def.37">Def37</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c7">H</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c6">G</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c5">F</font></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c5">F</font></span>)</span>
<b>by </b><i><a class="ref" href="autalg_1.html#T13" title="AUTALG_1:th.13">AUTALG_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c7">H</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span> <a href="altcat_2.html#K3" title="ALTCAT_2:func.3">**</a> the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#D37" target="_self" title="FUNCTOR0:def.37">Def37</a></i>
<br/>.= 
the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c7">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#D37" target="_self" title="FUNCTOR0:def.37">Def37</a></i>
;<br/>
<b>hence </b><a NAME="E3:98"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c6">G</font></span>)</span> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">H</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G</font> <a href="functor0.html#K13" title="FUNCTOR0:func.13">*</a> <font color="Maroon" title="c5">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="functor0.html#E1:98"><i><font color="Green" title="E63">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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