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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</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">Y</font>, <font color="Olive" title="b2">Z</font> being   <a href="waybel25.html#V1" title="WAYBEL25:attr.1">monotone-convergence</a>  <a href="t_0topsp.html#NM1" title="T_0TOPSP:NM.1">T_0-TopSpace</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">Y</font>,<font color="Olive" title="b2">Z</font> holds   <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b3">f</font>) is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">Y</font>, <font color="Maroon" title="c3">Z</font> be   <a href="waybel25.html#V1" title="WAYBEL25:attr.1">monotone-convergence</a>  <a href="t_0topsp.html#NM1" title="T_0TOPSP:NM.1">T_0-TopSpace</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="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">Y</font>,<font color="Maroon" title="c3">Z</font> holds   <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">f</font>) is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">Y</font>,<font color="Maroon" title="c3">Z</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">  <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>) is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel_0.html#D37" onmouseover="rs('waybel_0/D37')" onmouseout="rh()">WAYBEL_0:def 37</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"> ( <font color="Maroon" title="c5">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  or  not <font color="Maroon" title="c5">A</font> is  <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  or  <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>) <a href="waybel_0.html#R4" title="WAYBEL_0:pred.4">preserves_sup_of</a> <font color="Maroon" title="c5">A</font> )</span><br/>







<span class="kw">reconsider </span><font color="Maroon" title="c6">sA</font> =  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c5">A</font> as   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel26.html#T2" target="_self" onmouseover="rs('waybel26/T2')" onmouseout="rh()">Th2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">Xf</font> =  <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">sfA</font> =  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c5">A</font></span>)</span>, <font color="Maroon" title="c9">XfsA</font> = <span class="p1">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c5">A</font></span>)</span> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel26.html#T1" target="_self" onmouseover="rs('waybel26/T1')" onmouseout="rh()">Th1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">XZ</font> =  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Z</font>) as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>   <a href="waybel_0.html#V4" title="WAYBEL_0:attr.4">directed-sups-inheriting</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span> <a href="yellow_1.html#K5" title="YELLOW_1:func.5">|^</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel24.html#D3" onmouseover="rs('waybel24/D3')" onmouseout="rh()">WAYBEL24:def 3</a>, <a class="ref" href="waybel25.html#T43" onmouseover="rs('waybel25/T43')" onmouseout="rh()">WAYBEL25:43</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:21"/>
(  not <font color="Maroon" title="c5">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c5">A</font> is  <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</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">  <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>) <a href="waybel_0.html#R4" title="WAYBEL_0:pred.4">preserves_sup_of</a> <font color="Maroon" title="c5">A</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">A9</font> = <font color="Maroon" title="c5">A</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">fA9</font> = <span class="p1">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c11">A9</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Z</font>)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel26.html#T8" target="_self" onmouseover="rs('waybel26/T8')" onmouseout="rh()">Th8</a>, <a class="ref" href="yellow_2.html#T15" onmouseover="rs('yellow_2/T15')" onmouseout="rh()">YELLOW_2:15</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">XY</font> =  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>) as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>   <a href="waybel_0.html#V4" title="WAYBEL_0:attr.4">directed-sups-inheriting</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="yellow_1.html#K5" title="YELLOW_1:func.5">|^</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel24.html#D3" onmouseover="rs('waybel24/D3')" onmouseout="rh()">WAYBEL24:def 3</a>, <a class="ref" href="waybel25.html#T43" onmouseover="rs('waybel25/T43')" onmouseout="rh()">WAYBEL25:43</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">B</font> = <font color="Maroon" title="c11">A9</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c13">XY</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">B9</font> = <font color="Maroon" title="c14">B</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="yellow_1.html#K5" title="YELLOW_1:func.5">|^</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_2.html#T7" onmouseover="rs('yellow_2/T7')" onmouseout="rh()">YELLOW_2:7</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c16">fB</font> = <font color="Maroon" title="c12">fA9</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c10">XZ</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">fB9</font> = <font color="Maroon" title="c16">fB</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span> <a href="yellow_1.html#K5" title="YELLOW_1:func.5">|^</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_2.html#T7" onmouseover="rs('yellow_2/T7')" onmouseout="rh()">YELLOW_2:7</a></span>;<br/>
<span class="kw">assume </span><a NAME="E12:21"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c5">A</font>, <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel_0.html#D31" onmouseover="rs('waybel_0/D31')" onmouseout="rh()">WAYBEL_0:def 31</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"> (  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c5">A</font>, <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Z</font>) &amp;  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c5">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<font color="Maroon" title="c5">A</font>,<span class="p2">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>)</span>)</span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c18">I</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">J1</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">J2</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span>;<br/>
<a NAME="E13:21"/>
(  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span> #) &amp;  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">Z</font>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c3">Z</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span> #) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel25.html#D2" onmouseover="rs('waybel25/D2')" onmouseout="rh()">WAYBEL25:def 2</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c21">f9</font> = <font color="Maroon" title="c4">f</font> as   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow12.html#T36" onmouseover="rs('yellow12/T36')" onmouseout="rh()">YELLOW12:36</a></span>;<br/>
<a NAME="E15:21"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c17">fB9</font>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span> <a href="yellow_1.html#K5" title="YELLOW_1:func.5">|^</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T75" onmouseover="rs('waybel_0/T75')" onmouseout="rh()">WAYBEL_0:75</a></span>;<br/>
<a NAME="E16:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A1</font></span>: 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c17">fB9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c5">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T7" onmouseover="rs('waybel_0/T7')" onmouseout="rh()">WAYBEL_0:7</a></span>;<br/>
<a NAME="E17:21"/>
(  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Z</font>) is  <a href="waybel_0.html#V24" title="WAYBEL_0:attr.24">up-complete</a>  &amp; <font color="Maroon" title="c12">fA9</font> is  <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel26.html#T7" target="_self" onmouseover="rs('waybel26/T7')" onmouseout="rh()">Th7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:21"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c5">A</font>, <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Z</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T75" onmouseover="rs('waybel_0/T75')" onmouseout="rh()">WAYBEL_0:75</a></span>; <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">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c5">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<font color="Maroon" title="c5">A</font>,<span class="p2">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>)</span>)</span></span><br/>

<a NAME="E19:21"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span> <a href="yellow_1.html#K5" title="YELLOW_1:func.5">|^</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <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">X</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#D5" onmouseover="rs('yellow_1/D5')" onmouseout="rh()">YELLOW_1:def 5</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c22">fB99</font> = <font color="Maroon" title="c17">fB9</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p2">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span></span>)</span></span>)</span> ;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="21_1"><span class="kw">now </span> <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">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> holds   <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a>  <a href="waybel_3.html#K5" title="WAYBEL_3:func.5">pi</a> (<font color="Maroon" title="c22">fB99</font>,<font color="Olive" title="b1">x</font>),<span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span></span>)</span> <a href="yellow16.html#K2" title="YELLOW16:func.2">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c23">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</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">  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a>  <a href="waybel_3.html#K5" title="WAYBEL_3:func.5">pi</a> (<font color="Maroon" title="c22">fB99</font>,<font color="Maroon" title="c23">x</font>),<span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span></span>)</span> <a href="yellow16.html#K2" title="YELLOW16:func.2">.</a> <font color="Maroon" title="c23">x</font></span><br/><a NAME="E1:21_1"/>
( <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span></span>)</span> <a href="yellow16.html#K2" title="YELLOW16:func.2">.</a> <font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font> &amp;  <a href="waybel_3.html#K5" title="WAYBEL_3:func.5">pi</a> (<font color="Maroon" title="c22">fB99</font>,<font color="Maroon" title="c23">x</font>) is  <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a>, <a class="ref" href="yellow16.html#T35" onmouseover="rs('yellow16/T35')" onmouseout="rh()">YELLOW16:35</a></span>;<br/><span class="kw">hence </span><a NAME="E2:21_1"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a>  <a href="waybel_3.html#K5" title="WAYBEL_3:func.5">pi</a> (<font color="Maroon" title="c22">fB99</font>,<font color="Maroon" title="c23">x</font>),<span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span></span>)</span> <a href="yellow16.html#K2" title="YELLOW16:func.2">.</a> <font color="Maroon" title="c23">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T75" onmouseover="rs('waybel_0/T75')" onmouseout="rh()">WAYBEL_0:75</a></span>; <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/></div><span class="kw">end;</span></div>
<a NAME="E22:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A3</font></span>: 
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c22">fB99</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow16.html#T31" onmouseover="rs('yellow16/T31')" onmouseout="rh()">YELLOW16:31</a></span>;<br/>
<a NAME="E23:21"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="yellow_1.html#K5" title="YELLOW_1:func.5">|^</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <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">X</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#D5" onmouseover="rs('yellow_1/D5')" onmouseout="rh()">YELLOW_1:def 5</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c23">B99</font> = <font color="Maroon" title="c15">B9</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p2">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span></span>)</span> ;<br/>
<a NAME="E25:21"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c15">B9</font>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="yellow_1.html#K5" title="YELLOW_1:func.5">|^</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T75" onmouseover="rs('waybel_0/T75')" onmouseout="rh()">WAYBEL_0:75</a></span>;<br/>
<a NAME="E26:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A6</font></span>: 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c15">B9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c5">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T7" onmouseover="rs('waybel_0/T7')" onmouseout="rh()">WAYBEL_0:7</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="21_2"><span class="kw">now </span> <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">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Maroon" title="c8">sfA</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">XfsA</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c24">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</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"> <font color="Maroon" title="c8">sfA</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">XfsA</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font></span><br/><a NAME="E1:21_2"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span></span>)</span> <a href="yellow16.html#K2" title="YELLOW16:func.2">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c25">Bx</font> =  <a href="waybel_3.html#K5" title="WAYBEL_3:func.5">pi</a> (<font color="Maroon" title="c23">B99</font>,<font color="Maroon" title="c24">x</font>) as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow16.html#T35" onmouseover="rs('yellow16/T35')" onmouseout="rh()">YELLOW16:35</a></span>;<br/><a NAME="E3:21_2"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
( <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font></span>)</span></span>)</span> <a href="yellow16.html#K2" title="YELLOW16:func.2">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Z</font> &amp;  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c25">Bx</font>, <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Y</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a>, <a class="ref" href="waybel_0.html#T75" onmouseover="rs('waybel_0/T75')" onmouseout="rh()">WAYBEL_0:75</a></span>;<br/><a NAME="E4:21_2"/><span class="lab"><font color="Green" title="E23">A9</font></span>: 
<span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c23">B99</font></span>)</span> <a href="waybel_3.html#K4" title="WAYBEL_3:func.4">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K5" title="WAYBEL_3:func.5">pi</a> (<font color="Maroon" title="c23">B99</font>,<font color="Maroon" title="c24">x</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:21"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E23:21"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="yellow16.html#T33" onmouseover="rs('yellow16/T33')" onmouseout="rh()">YELLOW16:33</a></span>;<br/><a NAME="E5:21_2"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
( <font color="Maroon" title="c21">f9</font> <a href="waybel_0.html#R4" title="WAYBEL_0:pred.4">preserves_sup_of</a> <font color="Maroon" title="c25">Bx</font> &amp;  <a href="waybel_3.html#K5" title="WAYBEL_3:func.5">pi</a> (<font color="Maroon" title="c22">fB99</font>,<font color="Maroon" title="c24">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">f9</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c25">Bx</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel26.html#T12" target="_self" onmouseover="rs('waybel26/T12')" onmouseout="rh()">Th12</a>, <a class="ref" href="waybel_0.html#D37" onmouseover="rs('waybel_0/D37')" onmouseout="rh()">WAYBEL_0:def 37</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c8">sfA</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font> = 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K5" title="WAYBEL_3:func.5">pi</a> (<font color="Maroon" title="c22">fB99</font>,<font color="Maroon" title="c24">x</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:21"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E19:21"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E22:21"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="yellow16.html#T33" onmouseover="rs('yellow16/T33')" onmouseout="rh()">YELLOW16:33</a></span>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c25">Bx</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21_2"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E5:21_2"><span class="lab"><font color="Green" title="E24">A10</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">sA</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:21"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E23:21"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E4:21_2"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E1:21_2"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="funct_2.html#T15" onmouseover="rs('funct_2/T15')" onmouseout="rh()">FUNCT_2:15</a></span>
<br/>.= 
<font color="Maroon" title="c9">XfsA</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel26.html#D2" target="_self" onmouseover="rs('waybel26/D2')" onmouseout="rh()">Def2</a></span>
; <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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E28:21"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c5">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Z</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<font color="Maroon" title="c5">A</font>,<span class="p2">(<span class="default"><a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" onmouseover="rs('funct_2/T63')" onmouseout="rh()">FUNCT_2:63</a></span>; <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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