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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">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/><span class="kw">let </span><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" 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> 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/><span class="kw">let </span><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" 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">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/>





<span class="kw">set </span><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/>
<span class="kw">set </span><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/>
<span class="kw">reconsider </span><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> <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">let </span><font color="Maroon" title="c7">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" 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="c7">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="c7">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/>

<span class="kw">set </span><font color="Maroon" title="c8">F</font> =  <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c7">f</font>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">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> <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel26.html#T16" target="_self" onmouseover="rs('waybel26/T16')" onmouseout="rh()">Th16</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:27"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
<font color="Maroon" title="c7">f</font> is  <a href="borsuk_1.html#V3" title="BORSUK_1:attr.3">being_a_retraction</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="c7">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/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">Y9</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> <span class="kw">by</span> <span class="lab"><a class="txt" href="waybel26.html#E21"><span class="lab"><font color="Green" title="E19">Lm1</font></span></a></span>;<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">Y9</font>) is  <a href="waybel_0.html#V24" title="WAYBEL_0:attr.24">up-complete</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="E6:27"/>
 <a href="waybel26.html#K3" title="WAYBEL26:func.3">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c7">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel26.html#T13" target="_self" onmouseover="rs('waybel26/T13')" onmouseout="rh()">Th13</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="yellow16.html#D1" onmouseover="rs('yellow16/D1')" onmouseout="rh()">YELLOW16:def 1</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"> ( <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="c7">f</font>)</span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</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"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c9">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#D13" onmouseover="rs('yellow_0/D13')" onmouseout="rh()">YELLOW_0:def 13</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E23">A3</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="27_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="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">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> holds <br/><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="Olive" title="b1">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="c7">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="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="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="c7">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/><a NAME="E1:27_1"/><span class="lab"><font color="Green" title="E24">A4</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c7">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/><a NAME="E2:27_1"/><span class="lab"><font color="Green" title="E25">A5</font></span>: 
(  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c7">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="c7">f</font> is  <a href="quantal1.html#V11" title="QUANTAL1:attr.11">idempotent</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="yellow16.html#T44" onmouseover="rs('yellow16/T44')" onmouseout="rh()">YELLOW16:44</a>, <a class="ref" href="yellow16.html#T45" onmouseover="rs('yellow16/T45')" onmouseout="rh()">YELLOW16:45</a></span>;<br/><span class="kw">assume </span><a NAME="E3:27_1"/><span class="lab"><font color="Green" title="E26">A6</font></span>: 
<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" 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"> <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="c7">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/><span class="kw">then </span><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E22">A2</font></span></a></span>;<br/><span class="kw">reconsider </span><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> <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/><a NAME="E6:27_1"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="ref" href="waybel26.html#T2" target="_self" onmouseover="rs('waybel26/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E7:27_1"/><span class="kw">then </span>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" onmouseover="rs('relat_1/D19')" onmouseout="rh()">RELAT_1:def 19</a></span>;<br/><a NAME="E8:27_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="ref" href="yellow16.html#T4" onmouseover="rs('yellow16/T4')" onmouseout="rh()">YELLOW16:4</a></span>;<br/><span class="kw">hence </span><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="c7">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c13">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="ref" href="funct_1.html#T18" onmouseover="rs('funct_1/T18')" onmouseout="rh()">FUNCT_1:18</a></span>
<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="c7">f</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">a</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>
<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="c7">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>
;<br/> <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="E9:27"/>
<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="c7">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="ref" href="funct_2.html#T32" onmouseover="rs('funct_2/T32')" onmouseout="rh()">FUNCT_2:32</a></span>;<br/>
<a NAME="E10:27"/><span class="kw">then </span>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">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> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">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="c7">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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:27"/>
<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="c7">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:27"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="funct_1.html#T2" onmouseover="rs('funct_1/T2')" onmouseout="rh()">FUNCT_1:2</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="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="E12:27"/>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="waybel26.html#T17" target="_self" onmouseover="rs('waybel26/T17')" onmouseout="rh()">Th17</a>, <a class="ref" href="waybel25.html#T17" onmouseover="rs('waybel25/T17')" onmouseout="rh()">WAYBEL25:17</a></span>;<br/>
<a NAME="E13:27"/><span class="kw">then </span>
(  <a href="waybel26.html#K1" title="WAYBEL26:func.1">oContMaps</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c10">Y9</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#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> &amp; <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#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> 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#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>, <a class="ref" href="yellow16.html#T39" onmouseover="rs('yellow16/T39')" onmouseout="rh()">YELLOW16:39</a>, <a class="ref" href="yellow16.html#T42" onmouseover="rs('yellow16/T42')" onmouseout="rh()">YELLOW16:42</a></span>;<br/>
<a NAME="E14:27"/><span class="kw">then </span>
(  <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#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> &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#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#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>, <a class="ref" href="yellow16.html#T26" onmouseover="rs('yellow16/T26')" onmouseout="rh()">YELLOW16:26</a>, <a class="ref" href="yellow16.html#T27" onmouseover="rs('yellow16/T27')" onmouseout="rh()">YELLOW16:27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:27"/>
 <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#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 class="kw">by</span> <span class="lab"><a class="ref" href="waybel26.html#T16" target="_self" onmouseover="rs('waybel26/T16')" onmouseout="rh()">Th16</a>, <a class="ref" href="yellow16.html#T28" onmouseover="rs('yellow16/T28')" onmouseout="rh()">YELLOW16:28</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>
