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<span class="kw">let </span><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</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="c1">L1</font>,<font color="Maroon" title="c2">L2</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a>  &amp; <font color="Maroon" title="c1">L1</font> is  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>  &amp; <font color="Maroon" title="c1">L1</font> is  <a href="waybel_8.html#V3" title="WAYBEL_8:attr.3">arithmetic</a>  implies <font color="Maroon" title="c2">L2</font> is  <a href="waybel_8.html#V3" title="WAYBEL_8:attr.3">arithmetic</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:11"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> 
 <span class="kw">and </span><br/><a NAME="E2:11"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
( <font color="Maroon" title="c1">L1</font> is  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>  &amp; <font color="Maroon" title="c1">L1</font> is  <a href="waybel_8.html#V3" title="WAYBEL_8:attr.3">arithmetic</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="c2">L2</font> is  <a href="waybel_8.html#V3" title="WAYBEL_8:attr.3">arithmetic</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font><span class="kw"> such that </span><br/><a NAME="E4:11"/><span class="lab"><font color="Green" title="E12">A3</font></span>: 
<font color="Maroon" title="c3">f</font> is  <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E10">A1</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">g</font> = <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c1">L1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T67" onmouseover="rs('waybel_0/T67')" onmouseout="rh()">WAYBEL_0:67</a></span>;<br/>
<a NAME="E6:11"/><span class="lab"><font color="Green" title="E13">A4</font></span>: 
<font color="Maroon" title="c4">g</font> is  <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="waybel_0.html#T68" onmouseover="rs('waybel_0/T68')" onmouseout="rh()">WAYBEL_0:68</a></span>;<br/>
<a NAME="E7:11"/><span class="lab"><font color="Green" title="E14">A5</font></span>: 
<font color="Maroon" title="c2">L2</font> is   <a href="waybel_0.html#V24" title="WAYBEL_0:attr.24">up-complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="waybel13.html#T30" onmouseover="rs('waybel13/T30')" onmouseout="rh()">WAYBEL13:30</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="11_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">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">L2</font>  st <font color="Olive" title="b1">x2</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="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">L2</font></span>)</span> &amp; <font color="Olive" title="b2">y2</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="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">L2</font></span>)</span> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b1">x2</font>,<font color="Olive" title="b2">y2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L2</font> holds <br/> <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b1">x2</font>,<font color="Olive" title="b2">y2</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>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">L2</font></span>)</span></span></a><div class="add"><span class="kw">let </span><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">L2</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="c5">x2</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="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">L2</font></span>)</span> &amp; <font color="Maroon" title="c6">y2</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="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">L2</font></span>)</span> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L2</font> implies  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</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>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">L2</font></span>)</span> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:11_1"/><span class="lab"><font color="Green" title="E15">A6</font></span>: 
<font color="Maroon" title="c5">x2</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="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">L2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:11_1"/><span class="lab"><font color="Green" title="E16">A7</font></span>: 
<font color="Maroon" title="c6">y2</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="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">L2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:11_1"/><span class="lab"><font color="Green" title="E17">A8</font></span>: 
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L2</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#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</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>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">L2</font></span>)</span></span><br/><a NAME="E4:11_1"/>
<font color="Maroon" title="c5">x2</font> is  <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11_1"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="ref" href="waybel_8.html#D1" onmouseover="rs('waybel_8/D1')" onmouseout="rh()">WAYBEL_8:def 1</a></span>;<br/><a NAME="E5:11_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x2</font> is  <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E6:11"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E7:11"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="waybel13.html#T28" onmouseover="rs('waybel13/T28')" onmouseout="rh()">WAYBEL13:28</a></span>;<br/><a NAME="E6:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A9</font></span>: 
<font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x2</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="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c1">L1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_8.html#D1" onmouseover="rs('waybel_8/D1')" onmouseout="rh()">WAYBEL_8:def 1</a></span>;<br/><a NAME="E7:11_1"/>
<font color="Maroon" title="c6">y2</font> is  <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:11_1"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="ref" href="waybel_8.html#D1" onmouseover="rs('waybel_8/D1')" onmouseout="rh()">WAYBEL_8:def 1</a></span>;<br/><a NAME="E8:11_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">y2</font> is  <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E6:11"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E7:11"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="waybel13.html#T28" onmouseover="rs('waybel13/T28')" onmouseout="rh()">WAYBEL13:28</a></span>;<br/><a NAME="E9:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A10</font></span>: 
<font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">y2</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="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c1">L1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_8.html#D1" onmouseover="rs('waybel_8/D1')" onmouseout="rh()">WAYBEL_8:def 1</a></span>;<br/><a NAME="E10:11_1"/>
<font color="Maroon" title="c5">x2</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 <font color="Maroon" title="c2">L2</font>
 ;<br/><a NAME="E11:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A11</font></span>: 
<font color="Maroon" title="c5">x2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">g</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="E12:11_1"/><span class="lab"><font color="Green" title="E21">A12</font></span>: 
 <a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c1">L1</font> is  <a href="yellow_0.html#V5" title="YELLOW_0:attr.5">meet-inheriting</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="waybel_8.html#D5" onmouseover="rs('waybel_8/D5')" onmouseout="rh()">WAYBEL_8:def 5</a></span>;<br/><a NAME="E13:11_1"/>
<font color="Maroon" title="c6">y2</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 <font color="Maroon" title="c2">L2</font>
 ;<br/><a NAME="E14:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A13</font></span>: 
<font color="Maroon" title="c6">y2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">g</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="E15:11_1"/>
<font color="Maroon" title="c4">g</font> is  <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:11"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="waybel13.html#T20" onmouseover="rs('waybel13/T20')" onmouseout="rh()">WAYBEL13:20</a></span>;<br/><a NAME="E16:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A14</font></span>: 
<font color="Maroon" title="c4">g</font> <a href="waybel_0.html#R3" title="WAYBEL_0:pred.3">preserves_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</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="waybel_0.html#D32" onmouseover="rs('waybel_0/D32')" onmouseout="rh()">WAYBEL_0:def 32</a></span>;<br/><a NAME="E17:11_1"/><span class="kw">then </span>
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c4">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:11_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="ref" href="waybel_0.html#D30" onmouseover="rs('waybel_0/D30')" onmouseout="rh()">WAYBEL_0:def 30</a></span>;<br/><a NAME="E18:11_1"/><span class="kw">then </span>
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">y2</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:11_1"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="txt" href="#E14:11_1"><span class="lab"><font color="Green" title="E22">A13</font></span></a>, <a class="ref" href="funct_1.html#T60" onmouseover="rs('funct_1/T60')" onmouseout="rh()">FUNCT_1:60</a></span>;<br/><a NAME="E19:11_1"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">y2</font></span>)</span></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>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c1">L1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:11_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E9:11_1"><span class="lab"><font color="Green" title="E19">A10</font></span></a>, <a class="txt" href="#E12:11_1"><span class="lab"><font color="Green" title="E21">A12</font></span></a>, <a class="ref" href="yellow_0.html#D16" onmouseover="rs('yellow_0/D16')" onmouseout="rh()">YELLOW_0:def 16</a></span>;<br/><a NAME="E20:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A15</font></span>: 
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">y2</font></span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> is  <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_8.html#D1" onmouseover="rs('waybel_8/D1')" onmouseout="rh()">WAYBEL_8:def 1</a></span>;<br/><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span>)</span> = 
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:11_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E16:11_1"><span class="lab"><font color="Green" title="E23">A14</font></span></a>, <a class="ref" href="waybel_0.html#D30" onmouseover="rs('waybel_0/D30')" onmouseout="rh()">WAYBEL_0:def 30</a></span>
<br/>.= 
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">y2</font></span>)</span></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="#E11:11_1"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="txt" href="#E14:11_1"><span class="lab"><font color="Green" title="E22">A13</font></span></a>, <a class="ref" href="funct_1.html#T60" onmouseover="rs('funct_1/T60')" onmouseout="rh()">FUNCT_1:60</a></span>
;<br/><a NAME="E22:11_1"/><span class="kw">then </span>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> is  <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E6:11"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E7:11"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="txt" href="#E20:11_1"><span class="lab"><font color="Green" title="E24">A15</font></span></a>, <a class="ref" href="waybel13.html#T28" onmouseover="rs('waybel13/T28')" onmouseout="rh()">WAYBEL13:28</a></span>;<br/><span class="kw">hence </span><a NAME="E23:11_1"/>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">y2</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>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">L2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_8.html#D1" onmouseover="rs('waybel_8/D1')" onmouseout="rh()">WAYBEL_8:def 1</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><span class="kw">end;</span></div>
<a NAME="E9:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A16</font></span>: 
 <a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Maroon" title="c2">L2</font> is  <a href="yellow_0.html#V5" title="YELLOW_0:attr.5">meet-inheriting</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#D16" onmouseover="rs('yellow_0/D16')" onmouseout="rh()">YELLOW_0:def 16</a></span>;<br/>
<a NAME="E10:11"/>
<font color="Maroon" title="c2">L2</font> is  <a href="waybel_8.html#V2" title="WAYBEL_8:attr.2">algebraic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="waybel13.html#T32" onmouseover="rs('waybel13/T32')" onmouseout="rh()">WAYBEL13:32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:11"/>
<font color="Maroon" title="c2">L2</font> is  <a href="waybel_8.html#V3" title="WAYBEL_8:attr.3">arithmetic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:11"><span class="lab"><font color="Green" title="E15">A16</font></span></a>, <a class="ref" href="waybel_8.html#D5" onmouseover="rs('waybel_8/D5')" onmouseout="rh()">WAYBEL_8:def 5</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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