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<b>let </b><font color="Maroon" title="c1">Y</font>, <font color="Maroon" title="c2">Z</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">X</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>;<br/>



<a NAME="E1:24"/><i><font color="Green" title="E18">A1</font></i>: 
 <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">Y</font>,<font color="Maroon" title="c3">X</font> is <a href="waybel_0.html#V24" title="WAYBEL_0:attr.24">up-complete</a>
 
<b>by </b><i><a class="ref" href="waybel26.html#T8" target="_self" title="WAYBEL26:th.8">Th8</a></i>;<br/>
<b>let </b><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="c1">Y</font>,<font color="Maroon" title="c2">Z</font>;<br/><b>let </b><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="c2">Z</font>,<font color="Maroon" title="c3">X</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D37" title="WAYBEL_0:def.37">WAYBEL_0:def 37</a><br/>



<b>assume </b><a NAME="E2:24"/>
( 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> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c6">A'</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="c2">Z</font>,<font color="Maroon" title="c3">X</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c7">ZX</font> =  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c2">Z</font>,<font color="Maroon" title="c3">X</font> as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">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">X</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Z</font> <b>by </b><i><a class="txt" href="waybel26.html#E10"><i><font color="Green" title="E9">Lm1</font></i></a>, <a class="ref" href="waybel24.html#D3" title="WAYBEL24:def.3">WAYBEL24:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">B</font> = <font color="Maroon" title="c6">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 <font color="Maroon" title="c7">ZX</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c9">B'</font> = <font color="Maroon" title="c8">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="c3">X</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Z</font></span>)</span> <b>by </b><i><a class="ref" href="yellow_2.html#T7" title="YELLOW_2:th.7">YELLOW_2:7</a></i>;<br/>
<a NAME="E7:24"/><i><font color="Green" title="E19">A2</font></i>: 
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c9">B'</font>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Z</font>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T75" title="WAYBEL_0:th.75">WAYBEL_0:75</a></i>;<br/>
<a NAME="E8:24"/><b>then </b><i><font color="Green" title="E20">A3</font></i>: 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c9">B'</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>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T7" title="WAYBEL_0:th.7">WAYBEL_0:7</a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">fX</font> =  <a href="waybel26.html#K4" title="WAYBEL26:func.4">oContMaps</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</font>;<br/>
<a NAME="E9:24"/>
 <a href="waybel26.html#K4" title="WAYBEL26:func.4">oContMaps</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</font> is <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>
 
<b>by </b><i><a class="ref" href="waybel26.html#T11" target="_self" title="WAYBEL26:th.11">Th11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">fA'</font> = <span class="p1">(<span class="default"><a href="waybel26.html#K4" title="WAYBEL26:func.4">oContMaps</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c6">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">Y</font>,<font color="Maroon" title="c3">X</font></span>)</span> <b>by </b><i><a class="ref" href="yellow_2.html#T17" title="YELLOW_2:th.17">YELLOW_2:17</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">YX</font> =  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">Y</font>,<font color="Maroon" title="c3">X</font> as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">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">X</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font> <b>by </b><i><a class="txt" href="waybel26.html#E10"><i><font color="Green" title="E9">Lm1</font></i></a>, <a class="ref" href="waybel24.html#D3" title="WAYBEL24:def.3">WAYBEL24:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">fB</font> = <font color="Maroon" title="c11">fA'</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="c12">YX</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c14">fB'</font> = <font color="Maroon" title="c13">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">X</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font></span>)</span> <b>by </b><i><a class="ref" href="yellow_2.html#T7" title="YELLOW_2:th.7">YELLOW_2:7</a></i>;<br/>
<a NAME="E14:24"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c14">fB'</font>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T75" title="WAYBEL_0:th.75">WAYBEL_0:75</a></i>;<br/>
<a NAME="E15:24"/><b>then </b><i><font color="Green" title="E21">A4</font></i>: 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c14">fB'</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#K4" title="WAYBEL26:func.4">oContMaps</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c5">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T7" title="WAYBEL_0:th.7">WAYBEL_0:7</a></i>;<br/>
<b>assume </b><a NAME="E16:24"/>
 <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="c2">Z</font>,<font color="Maroon" title="c3">X</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D31" title="WAYBEL_0:def.31">WAYBEL_0:def 31</a><br/>

<a NAME="E17:24"/>
<font color="Maroon" title="c11">fA'</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>
 
;<br/>
<b>hence </b><a NAME="E18:24"/>
 <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#K4" title="WAYBEL26:func.4">oContMaps</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c5">A</font>, <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">Y</font>,<font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="waybel26.html#E1:24"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="waybel_0.html#T75" title="WAYBEL_0:th.75">WAYBEL_0:75</a></i>;<br/>

<b>reconsider </b><font color="Maroon" title="c15">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#K4" title="WAYBEL26:func.4">oContMaps</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c5">A</font></span>)</span>, <font color="Maroon" title="c16">XfsA</font> = <span class="p1">(<span class="default"><a href="waybel26.html#K4" title="WAYBEL26:func.4">oContMaps</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</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">Y</font>,<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span> <b>by </b><i><a class="ref" href="waybel26.html#T1" target="_self" title="WAYBEL26:th.1">Th1</a></i>;<br/>
<b>set </b><font color="Maroon" title="c17">I1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Z</font>;<br/>
<b>set </b><font color="Maroon" title="c18">I2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font>;<br/>
<b>set </b><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="c2">Z</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span>;<br/>
<b>set </b><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">Y</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span>;<br/>
<a NAME="E20:24"/><i><font color="Green" title="E22">A5</font></i>: 
<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</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">Y</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">Y</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#D5" title="YELLOW_1:def.5">YELLOW_1:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c21">fB''</font> = <font color="Maroon" title="c14">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">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</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">Y</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p3">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span></span>)</span></span>)</span> ;<br/>
<a NAME="E22:24"/><i><font color="Green" title="E23">A6</font></i>: 
<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Z</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="c2">Z</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="c2">Z</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#D5" title="YELLOW_1:def.5">YELLOW_1:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c22">B''</font> = <font color="Maroon" title="c9">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">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Z</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="c2">Z</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p3">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span></span>)</span></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c23">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="c2">Z</font>,<font color="Maroon" title="c3">X</font> <b>by </b><i><a class="ref" href="waybel26.html#T2" target="_self" title="WAYBEL26:th.2">Th2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>now </b></a><div class="add"><b>let </b><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">Y</font>;<br/><a NAME="E1:24_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">Y</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</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">X</font> &amp;  <a href="waybel_3.html#K5" title="WAYBEL_3:func.5">pi</a> <font color="Maroon" title="c21">fB''</font>,<font color="Maroon" title="c24">x</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> )
 <b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a>, <a class="ref" href="yellow16.html#T37" title="YELLOW16:th.37">YELLOW16:37</a></i>;<br/><b>hence </b><a NAME="E2:24_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="c21">fB''</font>,<font color="Maroon" title="c24">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">Y</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span></span>)</span> <a href="yellow16.html#K2" title="YELLOW16:func.2">.</a> <font color="Maroon" title="c24">x</font>
 <b>by </b><i><a class="ref" href="waybel_0.html#T75" title="WAYBEL_0:th.75">WAYBEL_0:75</a></i>;<br/></div><b>end;</b></div>
<a NAME="E26:24"/><b>then </b><i><font color="Green" title="E24">A7</font></i>: 
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c21">fB''</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</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">Y</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow16.html#T33" title="YELLOW16:th.33">YELLOW16:33</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2"><b>now </b></a><div class="add"><b>let </b><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">Y</font>;<br/><a NAME="E1:24_2"/><i><font color="Green" title="E25">A8</font></i>: 
( <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="c2">Z</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</font></span>)</span></span>)</span> <a href="yellow16.html#K2" title="YELLOW16:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font></span>)</span> <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">X</font> &amp; <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">Y</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p2">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">X</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">X</font> )
 <b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>;<br/><a NAME="E2:24_2"/><i><font color="Green" title="E26">A9</font></i>: 
 <a href="waybel_3.html#K5" title="WAYBEL_3:func.5">pi</a> <font color="Maroon" title="c21">fB''</font>,<font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel_3.html#K5" title="WAYBEL_3:func.5">pi</a> <font color="Maroon" title="c22">B''</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel26.html#T15" target="_self" title="WAYBEL26:th.15">Th15</a></i>;<br/><b>thus </b><font color="Maroon" title="c15">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="c21">fB''</font>,<font color="Maroon" title="c24">x</font></span>)</span>
<b>by </b><i><a class="txt" href="waybel26.html#E15:24"><i><font color="Green" title="E21">A4</font></i></a>, <a class="txt" href="waybel26.html#E20:24"><i><font color="Green" title="E22">A5</font></i></a>, <a class="txt" href="waybel26.html#E26:24"><i><font color="Green" title="E24">A7</font></i></a>, <a class="ref" href="yellow16.html#T35" title="YELLOW16:th.35">YELLOW16:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c22">B''</font></span>)</span> <a href="waybel_3.html#K7" title="WAYBEL_3:func.7">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font></span>)</span>
<b>by </b><i><a class="txt" href="waybel26.html#E7:24"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="waybel26.html#E22:24"><i><font color="Green" title="E23">A6</font></i></a>, <a class="txt" href="waybel26.html#E1:24_2"><i><font color="Green" title="E25">A8</font></i></a>, <a class="txt" href="waybel26.html#E2:24_2"><i><font color="Green" title="E26">A9</font></i></a>, <a class="ref" href="yellow16.html#T35" title="YELLOW16:th.35">YELLOW16:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c23">sA</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font>
<b>by </b><i><a class="txt" href="waybel26.html#E8:24"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="waybel26.html#E22:24"><i><font color="Green" title="E23">A6</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<font color="Maroon" title="c16">XfsA</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c24">x</font>
<b>by </b><i><a class="ref" href="waybel26.html#D3" target="_self" title="WAYBEL26:def.3">Def3</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E28:24"/>
 <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#K4" title="WAYBEL26:func.4">oContMaps</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel26.html#K4" title="WAYBEL26:func.4">oContMaps</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</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>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


</div>
