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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a> <a href="waybel_0.html#V24" title="WAYBEL_0:attr.24">up-complete</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</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">X</font> being <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">Y</font> being <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T</font>  st <font color="Olive" title="b1">X</font> is <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a> &amp; <font color="Olive" title="b2">Y</font> is <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a> holds <br/><span class="p1"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span> is <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a></span><br/><b>let </b><font color="Maroon" title="c3">X</font> be  <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</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">Y</font> being <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T</font>  st <font color="Maroon" title="c3">X</font> is <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a> &amp; <font color="Olive" title="b1">Y</font> is <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a> holds <br/><span class="p1"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Olive" title="b1">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span> is <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a></span><br/><b>let </b><font color="Maroon" title="c4">Y</font> be  <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">X</font> is <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a> &amp; <font color="Maroon" title="c4">Y</font> is <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a> implies <span class="p1"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span> is <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a> )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:61"/><i><font color="Green" title="E28">A1</font></i>: 
for <font color="Olive" title="b1">D</font> being 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="c1">S</font>  st  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Olive" title="b1">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> holds <br/><font color="Olive" title="b1">D</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">X</font>
 <b>and </b><br/><a NAME="E2:61"/><i><font color="Green" title="E29">A2</font></i>: 
for <font color="Olive" title="b1">D</font> being 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="c2">T</font>  st  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Olive" title="b1">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> holds <br/><font color="Olive" title="b1">D</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">Y</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel11.html#D1" title="WAYBEL11:def.1">WAYBEL11: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"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span> is <a href="waybel11.html#V1" title="WAYBEL11:attr.1">inaccessible_by_directed_joins</a></span><br/>

<b>let </b><font color="Maroon" title="c5">D</font> be  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"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel11.html#D1" title="WAYBEL11:def.1">WAYBEL11:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <font color="Maroon" title="c5">D</font>,<span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span> or  not <font color="Maroon" title="c5">D</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span> )</span><br/>

<b>assume </b><a NAME="E3:61"/><i><font color="Green" title="E30">A3</font></i>: 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c5">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c5">D</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span></span><br/>

<a NAME="E4:61"/><i><font color="Green" title="E31">A4</font></i>: 
( not  <a href="yellow_3.html#K4" title="YELLOW_3:func.4">proj1</a> <font color="Maroon" title="c5">D</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="yellow_3.html#K4" title="YELLOW_3:func.4">proj1</a> <font color="Maroon" title="c5">D</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> &amp; not  <a href="yellow_3.html#K5" title="YELLOW_3:func.5">proj2</a> <font color="Maroon" title="c5">D</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="yellow_3.html#K5" title="YELLOW_3:func.5">proj2</a> <font color="Maroon" title="c5">D</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> )
 
<b>by </b><i><a class="ref" href="yellow_3.html#T21" title="YELLOW_3:th.21">YELLOW_3:21</a>, <a class="ref" href="yellow_3.html#T22" title="YELLOW_3:th.22">YELLOW_3:22</a></i>;<br/>
<a NAME="E5:61"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c5">D</font>,<span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span>
 
<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="E6:61"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c5">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K4" title="YELLOW_3:func.4">proj1</a> <font color="Maroon" title="c5">D</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K5" title="YELLOW_3:func.5">proj2</a> <font color="Maroon" title="c5">D</font></span>)</span></span>)</span></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#T46" title="YELLOW_3:th.46">YELLOW_3:46</a></i>;<br/>
<a NAME="E7:61"/><b>then </b>
(  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><a href="yellow_3.html#K4" title="YELLOW_3:func.4">proj1</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> &amp;  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><a href="yellow_3.html#K5" title="YELLOW_3:func.5">proj2</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> )
 
<b>by </b><i><a class="txt" href="yellow10.html#E3:61"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E8:61"/><b>then </b><i><font color="Green" title="E32">A5</font></i>: 
(  <a href="yellow_3.html#K4" title="YELLOW_3:func.4">proj1</a> <font color="Maroon" title="c5">D</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">X</font> &amp;  <a href="yellow_3.html#K5" title="YELLOW_3:func.5">proj2</a> <font color="Maroon" title="c5">D</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">Y</font> )
 
<b>by </b><i><a class="txt" href="yellow10.html#E1:61"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="yellow10.html#E2:61"><i><font color="Green" title="E29">A2</font></i></a>, <a class="txt" href="yellow10.html#E4:61"><i><font color="Green" title="E31">A4</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">s</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E10:61"/><i><font color="Green" title="E33">A6</font></i>: 
( <font color="Maroon" title="c6">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_3.html#K4" title="YELLOW_3:func.4">proj1</a> <font color="Maroon" title="c5">D</font> &amp; <font color="Maroon" title="c6">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">t</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E12:61"/><i><font color="Green" title="E34">A7</font></i>: 
( <font color="Maroon" title="c7">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_3.html#K5" title="YELLOW_3:func.5">proj2</a> <font color="Maroon" title="c5">D</font> &amp; <font color="Maroon" title="c7">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> )
 <b>by </b><i><a class="txt" href="yellow10.html#E8:61"><i><font color="Green" title="E32">A5</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">s</font> = <font color="Maroon" title="c6">s</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> <b>by </b><i><a class="txt" href="yellow10.html#E10:61"><i><font color="Green" title="E33">A6</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">t</font> = <font color="Maroon" title="c7">t</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">T</font> <b>by </b><i><a class="txt" href="yellow10.html#E12:61"><i><font color="Green" title="E34">A7</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">s2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E16:61"/><i><font color="Green" title="E35">A8</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">s</font>,<font color="Maroon" title="c10">s2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font>
 <b>by </b><i><a class="txt" href="yellow10.html#E10:61"><i><font color="Green" title="E33">A6</font></i></a>, <a class="ref" href="relat_1.html#D4" title="RELAT_1:def.4">RELAT_1:def 4</a></i>;<br/>
<a NAME="E17:61"/><i><font color="Green" title="E36">A9</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#D2" title="YELLOW_3:def.2">YELLOW_3:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">s2</font> = <font color="Maroon" title="c10">s2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">T</font> <b>by </b><i><a class="txt" href="yellow10.html#E16:61"><i><font color="Green" title="E35">A8</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c12">t1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E20:61"/><i><font color="Green" title="E37">A10</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">t1</font>,<font color="Maroon" title="c9">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font>
 <b>by </b><i><a class="txt" href="yellow10.html#E12:61"><i><font color="Green" title="E34">A7</font></i></a>, <a class="ref" href="relat_1.html#D5" title="RELAT_1:def.5">RELAT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">t1</font> = <font color="Maroon" title="c12">t1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> <b>by </b><i><a class="txt" href="yellow10.html#E17:61"><i><font color="Green" title="E36">A9</font></i></a>, <a class="txt" href="yellow10.html#E20:61"><i><font color="Green" title="E37">A10</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c14">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span><b> such that </b><br/><a NAME="E23:61"/><i><font color="Green" title="E38">A11</font></i>: 
<font color="Maroon" title="c14">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font>
 <b>and </b><br/><a NAME="E24:61"/><i><font color="Green" title="E39">A12</font></i>: 
( <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c8">s</font>,<font color="Maroon" title="c11">s2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c14">z</font> &amp; <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c13">t1</font>,<font color="Maroon" title="c9">t</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c14">z</font> )
 <b>by </b><i><a class="txt" href="yellow10.html#E16:61"><i><font color="Green" title="E35">A8</font></i></a>, <a class="txt" href="yellow10.html#E20:61"><i><font color="Green" title="E37">A10</font></i></a>, <a class="ref" href="waybel_0.html#D1" title="WAYBEL_0:def.1">WAYBEL_0:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon" title="c15">z</font> = <font color="Maroon" title="c14">z</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font> &amp; <font color="Maroon" title="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span> )</span><br/><b>thus </b><a NAME="E1:61_1"/>
<font color="Maroon" title="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font>
 <b>by </b><i><a class="txt" href="yellow10.html#E23:61"><i><font color="Green" title="E38">A11</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span></span><br/><a NAME="E2:61_1"/><i><font color="Green" title="E40">A13</font></i>: 
<font color="Maroon" title="c15">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">z</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c15">z</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>
 <b>by </b><i><a class="txt" href="yellow10.html#E17:61"><i><font color="Green" title="E36">A9</font></i></a>, <a class="ref" href="mcart_1.html#T23" title="MCART_1:th.23">MCART_1:23</a></i>;<br/><a NAME="E3:61_1"/><b>then </b>
( <font color="Maroon" title="c8">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c15">z</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a>  &amp; <font color="Maroon" title="c9">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c15">z</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a>  )
 <b>by </b><i><a class="txt" href="yellow10.html#E24:61"><i><font color="Green" title="E39">A12</font></i></a>, <a class="ref" href="yellow_3.html#T11" title="YELLOW_3:th.11">YELLOW_3:11</a></i>;<br/><a NAME="E4:61_1"/><b>then </b>
( <font color="Maroon" title="c15">z</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c15">z</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> )
 <b>by </b><i><a class="txt" href="yellow10.html#E10:61"><i><font color="Green" title="E33">A6</font></i></a>, <a class="txt" href="yellow10.html#E12:61"><i><font color="Green" title="E34">A7</font></i></a>, <a class="ref" href="waybel_0.html#D20" title="WAYBEL_0:def.20">WAYBEL_0:def 20</a></i>;<br/><b>hence </b><a NAME="E5:61_1"/>
<font color="Maroon" title="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span>
 <b>by </b><i><a class="txt" href="yellow10.html#E2:61_1"><i><font color="Green" title="E40">A13</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</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><b>end;</b></div>
<b>hence </b><a NAME="E26:61"/>
not <font color="Maroon" title="c5">D</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="yellow_3.html#K12" title="YELLOW_3:func.12">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font></span><a href="yellow_3.html#K12" title="YELLOW_3:func.12">:]</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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