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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be  <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a> <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</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">x1</font>, <font color="Olive" title="b2">y1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b3">x2</font>, <font color="Olive" title="b4">y2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">T</font> holds  <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="Olive" title="b1">x1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b2">y1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">x2</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">y2</font></span>)</span></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <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"><font color="Olive" title="b1">x1</font>,<font color="Olive" title="b3">x2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Olive" title="b2">y1</font>,<font color="Olive" title="b4">y2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><br/><b>let </b><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">y1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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">x2</font>, <font color="Olive" title="b2">y2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">T</font> holds  <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="c3">x1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">y1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x2</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b2">y2</font></span>)</span></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <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"><font color="Maroon" title="c3">x1</font>,<font color="Olive" title="b1">x2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">y1</font>,<font color="Olive" title="b2">y2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><br/><b>let </b><font color="Maroon" title="c5">x2</font>, <font color="Maroon" title="c6">y2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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"> <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="c3">x1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">y1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x2</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">y2</font></span>)</span></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <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"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c5">x2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">y1</font>,<font color="Maroon" title="c6">y2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span><br/>





<a NAME="E1:18"/><i><font color="Green" title="E8">A1</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/>
<i><font color="Green" title="E9">A2</font></i>: <span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c5">x2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">y1</font>,<font color="Maroon" title="c6">y2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span>)</span> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c5">x2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">y1</font>,<font color="Maroon" title="c6">y2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="yellow10.html#T14" target="_self" title="YELLOW10:th.14">Th14</a></i>
<br/>.= 
<font color="Maroon" title="c3">x1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">y1</font>,<font color="Maroon" title="c6">y2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<font color="Maroon" title="c3">x1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">y1</font>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<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="c3">x1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">y1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x2</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">y2</font></span>)</span></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c5">x2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">y1</font>,<font color="Maroon" title="c6">y2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span></span>)</span> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c5">x2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">y1</font>,<font color="Maroon" title="c6">y2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="yellow10.html#T14" target="_self" title="YELLOW10:th.14">Th14</a></i>
<br/>.= 
<font color="Maroon" title="c5">x2</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">y1</font>,<font color="Maroon" title="c6">y2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<font color="Maroon" title="c5">x2</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">y2</font>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<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="c3">x1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">y1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x2</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">y2</font></span>)</span></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
;<br/>
<b>hence </b><a NAME="E4:18"/>
<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="c3">x1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">y1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x2</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">y2</font></span>)</span></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <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"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c5">x2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c4">y1</font>,<font color="Maroon" title="c6">y2</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span>
 <b>by </b><i><a class="txt" href="yellow10.html#E1:18"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="yellow10.html#E2:18"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="domain_1.html#T12" title="DOMAIN_1:th.12">DOMAIN_1:12</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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