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<span class="kw">let </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="yellow_0.html#D17" onmouseover="rs('yellow_0/D17')" onmouseout="rh()">YELLOW_0:def 17</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"> (  not <font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI: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="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span> or  not <font color="Maroon" title="c5">y</font> <a href="tarski.html#R2" title="TARSKI: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="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span> or  not  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> or  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font>) <a href="tarski.html#R2" title="TARSKI: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="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">ab</font> =  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:27_1_1"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI: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="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:27_1_1"/><span class="lab"><font color="Green" title="E15">A2</font></span>: 
<font color="Maroon" title="c5">y</font> <a href="tarski.html#R2" title="TARSKI: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="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:27_1_1"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</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">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font>) <a href="tarski.html#R2" title="TARSKI: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="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span></span><br/>

<a NAME="E4:27_1_1"/><span class="lab"><font color="Green" title="E16">A3</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1_1"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="yellow_0.html#D15" onmouseover="rs('yellow_0/D15')" onmouseout="rh()">YELLOW_0:def 15</a></span>;<br/>
<a NAME="E5:27_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A4</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#D4" target="_self" onmouseover="rs('yellow11/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<a NAME="E6:27_1_1"/><span class="lab"><font color="Green" title="E18">A5</font></span>: 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T41" onmouseover="rs('yellow_0/T41')" onmouseout="rh()">YELLOW_0:41</a></span>;<br/>
<a NAME="E7:27_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T22" onmouseover="rs('yellow_0/T22')" onmouseout="rh()">YELLOW_0:22</a></span>;<br/>
<a NAME="E8:27_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A6</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:27_1_1"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="ref" href="yellow_0.html#D2" onmouseover="rs('yellow_0/D2')" onmouseout="rh()">YELLOW_0:def 2</a></span>;<br/>
<a NAME="E9:27_1_1"/>
<font color="Maroon" title="c5">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1_1"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="ref" href="yellow_0.html#D15" onmouseover="rs('yellow_0/D15')" onmouseout="rh()">YELLOW_0:def 15</a></span>;<br/>
<a NAME="E10:27_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A7</font></span>: 
<font color="Maroon" title="c5">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow11.html#D4" target="_self" onmouseover="rs('yellow11/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<a NAME="E11:27_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:27_1_1"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="ref" href="yellow11.html#D4" target="_self" onmouseover="rs('yellow11/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<a NAME="E12:27_1_1"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:27_1_1"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E6:27_1_1"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="ref" href="yellow_0.html#T22" onmouseover="rs('yellow_0/T22')" onmouseout="rh()">YELLOW_0:22</a></span>;<br/>
<a NAME="E13:27_1_1"/><span class="kw">then </span>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:27_1_1"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="ref" href="yellow11.html#D4" target="_self" onmouseover="rs('yellow11/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:27_1_1"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font>) <a href="tarski.html#R2" title="TARSKI: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="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#D15" onmouseover="rs('yellow_0/D15')" onmouseout="rh()">YELLOW_0:def 15</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/>


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