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<div class="add">

<b>let </b><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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">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="b2">Y</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Olive" title="b1">Z</font><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">Z</font>,<font color="Olive" title="b2">Y</font>  st <font color="Olive" title="b3">f</font> is <a href="borsuk_1.html#V3" title="BORSUK_1:attr.3">being_a_retraction</a> holds <br/> <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> <a href="yellow16.html#R1" title="YELLOW16:pred.1">is_a_retraction_of</a>  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">Z</font>, <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b2">Y</font></span><br/><b>let </b><font color="Maroon" title="c2">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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Y</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c2">Z</font><br/> for <font color="Olive" title="b2">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">Z</font>,<font color="Olive" title="b1">Y</font>  st <font color="Olive" title="b2">f</font> is <a href="borsuk_1.html#V3" title="BORSUK_1:attr.3">being_a_retraction</a> holds <br/> <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b2">f</font> <a href="yellow16.html#R1" title="YELLOW16:pred.1">is_a_retraction_of</a>  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Z</font>, <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">Y</font></span><br/><b>let </b><font color="Maroon" title="c3">Y</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c2">Z</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">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">Z</font>,<font color="Maroon" title="c3">Y</font>  st <font color="Olive" title="b1">f</font> is <a href="borsuk_1.html#V3" title="BORSUK_1:attr.3">being_a_retraction</a> holds <br/> <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> <a href="yellow16.html#R1" title="YELLOW16:pred.1">is_a_retraction_of</a>  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Z</font>, <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Y</font></span><br/>





<b>set </b><font color="Maroon" title="c4">XY</font> =  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Y</font>;<br/>
<b>set </b><font color="Maroon" title="c5">XZ</font> =  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Z</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">uXZ</font> =  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Z</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="waybel_0.html#V24" title="WAYBEL_0:attr.24">up-complete</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a> <b>by </b><i><a class="ref" href="waybel26.html#T8" target="_self" title="WAYBEL26:th.8">Th8</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">sXY</font> =  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">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="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c6">uXZ</font> <b>by </b><i><a class="ref" href="waybel26.html#T17" target="_self" title="WAYBEL26:th.17">Th17</a></i>;<br/>
<b>let </b><font color="Maroon" title="c8">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">Z</font>,<font color="Maroon" title="c3">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">f</font> is <a href="borsuk_1.html#V3" title="BORSUK_1:attr.3">being_a_retraction</a> implies  <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c8">f</font> <a href="yellow16.html#R1" title="YELLOW16:pred.1">is_a_retraction_of</a>  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Z</font>, <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Y</font> )</span><br/>

<b>assume </b><a NAME="E3:27"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c8">f</font> is <a href="borsuk_1.html#V3" title="BORSUK_1:attr.3">being_a_retraction</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="c8">f</font> <a href="yellow16.html#R1" title="YELLOW16:pred.1">is_a_retraction_of</a>  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Z</font>, <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Y</font></span><br/>

<b>set </b><font color="Maroon" title="c9">F</font> =  <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c8">f</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">Y'</font> = <font color="Maroon" title="c3">Y</font> as  <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> <b>by </b><i><a class="txt" href="#E3:27"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="waybel26.html#E22"><i><font color="Green" title="E19">Lm1</font></i></a></i>;<br/>
<a NAME="E5:27"/>
 <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c10">Y'</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>hence </b><a NAME="E6:27"/>
 <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c8">f</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</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">Z</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">Y</font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel26.html#T14" target="_self" title="WAYBEL26:th.14">Th14</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow16.html#D1" title="YELLOW16:def.1">YELLOW16:def 1</a> <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"><a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c8">f</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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">Y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <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">Y</font></span>)</span> &amp;  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Y</font> is    <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Z</font> )</span><br/>

<a NAME="E7:27"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <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="c3">Y</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></i>;<br/>
<a NAME="E8:27"/><i><font color="Green" title="E23">A3</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">sXY</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">uXZ</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D13" title="YELLOW_0:def.13">YELLOW_0:def 13</a></i>;<br/>
<a NAME="E9:27"/><b>then </b>
<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="c8">f</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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">Y</font></span>)</span> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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">Y</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T38" title="FUNCT_2:th.38">FUNCT_2:38</a></i>;<br/>
<a NAME="E10:27"/><b>then </b><i><font color="Green" title="E24">A4</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</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="c8">f</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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="c3">Y</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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">Y</font></span>)</span> implies <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <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="c3">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.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="c8">f</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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="c3">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> )</span><br/><b>assume </b><a NAME="E1:27_1"/><i><font color="Green" title="E25">A5</font></i>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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">Y</font></span>)</span>
 ; <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"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <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="c3">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.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="c8">f</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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="c3">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span><br/><b>then reconsider </b><font color="Maroon" title="c12">a</font> = <font color="Maroon" title="c11">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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">Z</font></span>)</span> <b>by </b><i><a class="txt" href="#E8:27"><i><font color="Green" title="E23">A3</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">a</font> = <font color="Maroon" title="c12">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">Z</font> <b>by </b><i><a class="ref" href="waybel26.html#T2" target="_self" title="WAYBEL26:th.2">Th2</a></i>;<br/><a NAME="E4:27_1"/><i><font color="Green" title="E26">A6</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c8">f</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="c3">Y</font> &amp; <font color="Maroon" title="c11">x</font> is   <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="c3">Y</font> )
 <b>by </b><i><a class="txt" href="#E3:27"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="#E1:27_1"><i><font color="Green" title="E25">A5</font></i></a>, <a class="ref" href="waybel26.html#T2" target="_self" title="WAYBEL26:th.2">Th2</a>, <a class="ref" href="yellow16.html#T46" title="YELLOW16:th.46">YELLOW16:46</a></i>;<br/><a NAME="E5:27_1"/><b>then </b>
( <font color="Maroon" title="c8">f</font> is <a href="quantal1.html#V11" title="QUANTAL1:attr.11">idempotent</a> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c13">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">Y</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c8">f</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> )
 <b>by </b><i><a class="txt" href="#E3:27"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a>, <a class="ref" href="yellow16.html#T47" title="YELLOW16:th.47">YELLOW16:47</a></i>;<br/><a NAME="E6:27_1"/><b>then </b>
<font color="Maroon" title="c8">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c13">a</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c13">a</font>
 <b>by </b><i><a class="txt" href="#E4:27_1"><i><font color="Green" title="E26">A6</font></i></a>, <a class="ref" href="yellow16.html#T4" title="YELLOW16:th.4">YELLOW16:4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <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="c3">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> = 
<font color="Maroon" title="c8">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c13">a</font>
<b>by </b><i><a class="txt" href="#E1:27_1"><i><font color="Green" title="E25">A5</font></i></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>
<br/>.= 
<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="c8">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">a</font>
<b>by </b><i><a class="ref" href="waybel26.html#D2" target="_self" title="WAYBEL26:def.2">Def2</a></i>
<br/>.= 
<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="c8">f</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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="c3">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
<b>by </b><i><a class="txt" href="#E1:27_1"><i><font color="Green" title="E25">A5</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:27"/>
<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="c8">f</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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">Y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <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">Y</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E7:27"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="#E10:27"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Y</font> is    <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Z</font></span><br/>

<a NAME="E13:27"/><i><font color="Green" title="E25">A7</font></i>: 
 <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c10">Y'</font> is  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">Y</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">X</font>
 
<b>by </b><i><a class="ref" href="waybel24.html#D3" title="WAYBEL24:def.3">WAYBEL24:def 3</a>, <a class="ref" href="waybel25.html#T43" title="WAYBEL25:th.43">WAYBEL25:43</a></i>;<br/>
<a NAME="E14:27"/><i><font color="Green" title="E26">A8</font></i>: 
 <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Z</font> is  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">Z</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">X</font>
 
<b>by </b><i><a class="ref" href="waybel24.html#D3" title="WAYBEL24:def.3">WAYBEL24:def 3</a>, <a class="ref" href="waybel25.html#T43" title="WAYBEL25:th.43">WAYBEL25:43</a></i>;<br/>
<a NAME="E15:27"/>
 <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Y</font> is  <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  <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c2">Z</font>
 
<b>by </b><i><a class="txt" href="#E3:27"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="waybel26.html#T18" target="_self" title="WAYBEL26:th.18">Th18</a>, <a class="ref" href="waybel25.html#T17" title="WAYBEL25:th.17">WAYBEL25:17</a></i>;<br/>
<a NAME="E16:27"/><b>then </b>
<span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c3">Y</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">X</font> is  <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">Z</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">X</font>
 
<b>by </b><i><a class="ref" href="yellow16.html#T41" title="YELLOW16:th.41">YELLOW16:41</a>, <a class="ref" href="yellow16.html#T44" title="YELLOW16:th.44">YELLOW16:44</a></i>;<br/>
<a NAME="E17:27"/><b>then </b>
 <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Y</font> is  <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">Z</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">X</font>
 
<b>by </b><i><a class="txt" href="#E13:27"><i><font color="Green" title="E25">A7</font></i></a>, <a class="ref" href="yellow16.html#T28" title="YELLOW16:th.28">YELLOW16:28</a>, <a class="ref" href="yellow16.html#T29" title="YELLOW16:th.29">YELLOW16:29</a></i>;<br/>
<b>hence </b><a NAME="E18:27"/>
 <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">Y</font> is  <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  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Z</font>
 <b>by </b><i><a class="txt" href="#E14:27"><i><font color="Green" title="E26">A8</font></i></a>, <a class="ref" href="waybel26.html#T17" target="_self" title="WAYBEL26:th.17">Th17</a>, <a class="ref" href="yellow16.html#T30" title="YELLOW16:th.30">YELLOW16:30</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
