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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">L</font> be  <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>;<br/><b>let </b><font color="Maroon" title="c3">d</font> be   <a href="lattice5.html#NM4" title="LATTICE5:NM.4">distance_function</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">L</font>;<br/><b>let </b><font color="Maroon" title="c4">Aq</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c5">dq</font> be   <a href="lattice5.html#NM4" title="LATTICE5:NM.4">distance_function</a> of <font color="Maroon" title="c4">Aq</font>,<font color="Maroon" title="c2">L</font>;<br/>









<b>assume </b><a NAME="E1:47"/>
<font color="Maroon" title="c4">Aq</font>,<font color="Maroon" title="c5">dq</font> <a href="lattice8.html#R2" title="LATTICE8:pred.2">is_extension2_of</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">d</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">q</font> being    <a href="lattice5.html#M1" title="LATTICE5:mode.1">QuadrSeq</a> of <font color="Maroon" title="c3">d</font><b> such that </b><br/><a NAME="E3:47"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon" title="c4">Aq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice8.html#K7" title="LATTICE8:func.7">NextSet2</a> <font color="Maroon" title="c3">d</font>
 <b>and </b><br/><a NAME="E4:47"/><i><font color="Green" title="E37">A2</font></i>: 
<font color="Maroon" title="c5">dq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice8.html#K8" title="LATTICE8:func.8">NextDelta2</a> <font color="Maroon" title="c6">q</font>
 <b>by </b><i><a class="ref" href="lattice8.html#D11" target="_self" title="LATTICE8:def.11">Def11</a></i>;<br/>
<b>let </b><font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c8">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font>;<br/>



<b>assume </b><a NAME="E5:47"/><i><font color="Green" title="E38">A3</font></i>: 
<font color="Maroon" title="c3">d</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c8">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c10">b</font>
 ;<br/>

<a NAME="E6:47"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Olive" title="b1">x'</font>,<font color="Olive" title="b2">y'</font>,<font color="Olive" title="b3">a'</font>,<font color="Olive" title="b4">b'</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> where <font color="Olive" title="b1">x'</font>, <font color="Olive" title="b2">y'</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>, <font color="Olive" title="b3">a'</font>, <font color="Olive" title="b4">b'</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> : <font color="Maroon" title="c3">d</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Olive" title="b1">x'</font>,<font color="Olive" title="b2">y'</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b3">a'</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">b'</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="lattice5.html#D14" title="LATTICE5:def.14">LATTICE5:def 14</a></i>;<br/>
<a NAME="E7:47"/><b>then </b>
<span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c8">y</font>,<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">q</font>
 
<b>by </b><i><a class="txt" href="lattice8.html#E5:47"><i><font color="Green" title="E38">A3</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">o</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E9:47"/><i><font color="Green" title="E39">A4</font></i>: 
( <font color="Maroon" title="c11">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q</font> &amp; <font color="Maroon" title="c6">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c8">y</font>,<font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">o</font> = <font color="Maroon" title="c11">o</font> as   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> <b>by </b><i><a class="txt" href="lattice8.html#E9:47"><i><font color="Green" title="E39">A4</font></i></a>, <a class="ref" href="ordinal1.html#T23" title="ORDINAL1:th.23">ORDINAL1:23</a></i>;<br/>
<a NAME="E11:47"/><i><font color="Green" title="E40">A5</font></i>: 
<font color="Maroon" title="c6">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice8.html#K4" title="LATTICE8:func.4">Quadr2</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c12">o</font>
 
<b>by </b><i><a class="txt" href="lattice8.html#E9:47"><i><font color="Green" title="E39">A4</font></i></a>, <a class="ref" href="lattice8.html#D7" target="_self" title="LATTICE8:def.7">Def7</a></i>;<br/>
<a NAME="E12:47"/><b>then </b><i><font color="Green" title="E41">A6</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lattice8.html#K4" title="LATTICE8:func.4">Quadr2</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c12">o</font></span>)</span> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> 
 
<b>by </b><i><a class="txt" href="lattice8.html#E9:47"><i><font color="Green" title="E39">A4</font></i></a>, <a class="ref" href="mcart_1.html#T78" title="MCART_1:th.78">MCART_1:78</a></i>;<br/>
<a NAME="E13:47"/><i><font color="Green" title="E42">A7</font></i>: 
<font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lattice8.html#K4" title="LATTICE8:func.4">Quadr2</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c12">o</font></span>)</span> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> 
 
<b>by </b><i><a class="txt" href="lattice8.html#E9:47"><i><font color="Green" title="E39">A4</font></i></a>, <a class="txt" href="lattice8.html#E11:47"><i><font color="Green" title="E40">A5</font></i></a>, <a class="ref" href="mcart_1.html#T78" title="MCART_1:th.78">MCART_1:78</a></i>;<br/>
<a NAME="E14:47"/><i><font color="Green" title="E43">A8</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lattice8.html#K4" title="LATTICE8:func.4">Quadr2</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c12">o</font></span>)</span> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a> 
 
<b>by </b><i><a class="txt" href="lattice8.html#E9:47"><i><font color="Green" title="E39">A4</font></i></a>, <a class="txt" href="lattice8.html#E11:47"><i><font color="Green" title="E40">A5</font></i></a>, <a class="ref" href="mcart_1.html#T78" title="MCART_1:th.78">MCART_1:78</a></i>;<br/>
<a NAME="E15:47"/><i><font color="Green" title="E44">A9</font></i>: 
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lattice8.html#K4" title="LATTICE8:func.4">Quadr2</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c12">o</font></span>)</span> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a> 
 
<b>by </b><i><a class="txt" href="lattice8.html#E9:47"><i><font color="Green" title="E39">A4</font></i></a>, <a class="txt" href="lattice8.html#E11:47"><i><font color="Green" title="E40">A5</font></i></a>, <a class="ref" href="mcart_1.html#T78" title="MCART_1:th.78">MCART_1:78</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">B</font> =  <a href="lattice8.html#K3" title="LATTICE8:func.3">ConsecutiveSet2</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c12">o</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c14">Q</font> =  <a href="lattice8.html#K4" title="LATTICE8:func.4">Quadr2</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c12">o</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default"><font color="Maroon" title="c13">B</font>,<font color="Maroon" title="c13">B</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c15">cd</font> =  <a href="lattice8.html#K6" title="LATTICE8:func.6">ConsecutiveDelta2</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c12">o</font> as   <a href="lattice5.html#NM3" title="LATTICE5:NM.3">BiFunction</a> of <font color="Maroon" title="c13">B</font>,<font color="Maroon" title="c2">L</font> ;<br/>
<a NAME="E19:47"/>
( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">B</font> )
 
<b>by </b><i><a class="ref" href="lattice8.html#T18" target="_self" title="LATTICE8:th.18">Th18</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c16">xo</font> = <font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c17">yo</font> = <font color="Maroon" title="c8">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c13">B</font> ;<br/>
<a NAME="E21:47"/>
( <font color="Maroon" title="c16">xo</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">B</font> &amp; <font color="Maroon" title="c17">yo</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">B</font> &amp; <font color="Maroon" title="c13">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice8.html#K1" title="LATTICE8:func.1">new_set2</a> <font color="Maroon" title="c13">B</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c18">x1</font> = <font color="Maroon" title="c16">xo</font>, <font color="Maroon" title="c19">y1</font> = <font color="Maroon" title="c17">yo</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="lattice8.html#K1" title="LATTICE8:func.1">new_set2</a> <font color="Maroon" title="c13">B</font> ;<br/>
<a NAME="E23:47"/><i><font color="Green" title="E45">A10</font></i>: 
 <a href="lattice8.html#K3" title="LATTICE8:func.3">ConsecutiveSet2</a> <font color="Maroon" title="c1">A</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c12">o</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice8.html#K1" title="LATTICE8:func.1">new_set2</a> <font color="Maroon" title="c13">B</font>
 
<b>by </b><i><a class="ref" href="lattice8.html#T16" target="_self" title="LATTICE8:th.16">Th16</a></i>;<br/>
<a NAME="E24:47"/>
<font color="Maroon" title="c12">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lattice5.html#K8" title="LATTICE5:func.8">DistEsti</a> <font color="Maroon" title="c3">d</font>
 
<b>by </b><i><a class="txt" href="lattice8.html#E9:47"><i><font color="Green" title="E39">A4</font></i></a>, <a class="ref" href="lattice5.html#T28" title="LATTICE5:th.28">LATTICE5:28</a></i>;<br/>
<a NAME="E25:47"/><b>then </b><i><font color="Green" title="E46">A11</font></i>: 
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c12">o</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="lattice5.html#K8" title="LATTICE5:func.8">DistEsti</a> <font color="Maroon" title="c3">d</font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#T33" title="ORDINAL1:th.33">ORDINAL1:33</a></i>;<br/>
<a NAME="E26:47"/><b>then </b><i><font color="Green" title="E47">A12</font></i>: 
 <a href="lattice8.html#K6" title="LATTICE8:func.6">ConsecutiveDelta2</a> <font color="Maroon" title="c6">q</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c12">o</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="lattice8.html#K6" title="LATTICE8:func.6">ConsecutiveDelta2</a> <font color="Maroon" title="c6">q</font>,<span class="p1">(<span class="default"><a href="lattice5.html#K8" title="LATTICE5:func.8">DistEsti</a> <font color="Maroon" title="c3">d</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice8.html#T25" target="_self" title="LATTICE8:th.25">Th25</a></i>;<br/>
<i><font color="Green" title="E48">A13</font></i>:  <a href="lattice8.html#K6" title="LATTICE8:func.6">ConsecutiveDelta2</a> <font color="Maroon" title="c6">q</font>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Maroon" title="c12">o</font></span>)</span> = 
 <a href="lattice8.html#K2" title="LATTICE8:func.2">new_bi_fun2</a> <span class="p1">(<span class="default"><a href="lattice5.html#K11" title="LATTICE5:func.11">BiFun</a> <span class="p2">(<span class="default"><a href="lattice8.html#K6" title="LATTICE8:func.6">ConsecutiveDelta2</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c12">o</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice8.html#K3" title="LATTICE8:func.3">ConsecutiveSet2</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c12">o</font></span>)</span>,<font color="Maroon" title="c2">L</font></span>)</span>,<span class="p1">(<span class="default"><a href="lattice8.html#K4" title="LATTICE8:func.4">Quadr2</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c12">o</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice8.html#T20" target="_self" title="LATTICE8:th.20">Th20</a></i>
<br/>.= 
 <a href="lattice8.html#K2" title="LATTICE8:func.2">new_bi_fun2</a> <font color="Maroon" title="c15">cd</font>,<font color="Maroon" title="c14">Q</font>
<b>by </b><i><a class="ref" href="lattice5.html#D16" title="LATTICE5:def.16">LATTICE5:def 16</a></i>
;<br/>
<a NAME="E28:47"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E29:47"/><b>then </b><i><font color="Green" title="E49">A14</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E30:47"/><i><font color="Green" title="E50">A15</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E31:47"/><b>then </b><i><font color="Green" title="E51">A16</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E32:47"/><i><font color="Green" title="E52">A17</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lattice8.html#K1" title="LATTICE8:func.1">new_set2</a> <font color="Maroon" title="c13">B</font>
 
<b>by </b><i><a class="txt" href="lattice8.html#E30:47"><i><font color="Green" title="E50">A15</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E33:47"/><i><font color="Green" title="E53">A18</font></i>: 
<font color="Maroon" title="c15">cd</font> is <a href="lattice5.html#V2" title="LATTICE5:attr.2">zeroed</a>
 
<b>by </b><i><a class="ref" href="lattice8.html#T26" target="_self" title="LATTICE8:th.26">Th26</a></i>;<br/>
<a NAME="E34:47"/><i><font color="Green" title="E54">A19</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="lattice8.html#K2" title="LATTICE8:func.2">new_bi_fun2</a> <font color="Maroon" title="c15">cd</font>,<font color="Maroon" title="c14">Q</font></span>)</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"><span class="p2">(<span class="default"><a href="lattice8.html#K1" title="LATTICE8:func.1">new_set2</a> <font color="Maroon" title="c13">B</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattice8.html#K1" title="LATTICE8:func.1">new_set2</a> <font color="Maroon" title="c13">B</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E35:47"/><b>then </b><i><font color="Green" title="E55">A20</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c18">x1</font>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="lattice8.html#K2" title="LATTICE8:func.2">new_bi_fun2</a> <font color="Maroon" title="c15">cd</font>,<font color="Maroon" title="c14">Q</font></span>)</span>
 
<b>by </b><i><a class="txt" href="lattice8.html#E29:47"><i><font color="Green" title="E49">A14</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E36:47"/><i><font color="Green" title="E56">A21</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="lattice8.html#K2" title="LATTICE8:func.2">new_bi_fun2</a> <font color="Maroon" title="c15">cd</font>,<font color="Maroon" title="c14">Q</font></span>)</span>
 
<b>by </b><i><a class="txt" href="lattice8.html#E29:47"><i><font color="Green" title="E49">A14</font></i></a>, <a class="txt" href="lattice8.html#E32:47"><i><font color="Green" title="E52">A17</font></i></a>, <a class="txt" href="lattice8.html#E34:47"><i><font color="Green" title="E54">A19</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E37:47"/><i><font color="Green" title="E57">A22</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c19">y1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="lattice8.html#K2" title="LATTICE8:func.2">new_bi_fun2</a> <font color="Maroon" title="c15">cd</font>,<font color="Maroon" title="c14">Q</font></span>)</span>
 
<b>by </b><i><a class="txt" href="lattice8.html#E31:47"><i><font color="Green" title="E51">A16</font></i></a>, <a class="txt" href="lattice8.html#E34:47"><i><font color="Green" title="E54">A19</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E38:47"/><i><font color="Green" title="E58">A23</font></i>: 
<font color="Maroon" title="c3">d</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c15">cd</font>
 
<b>by </b><i><a class="ref" href="lattice8.html#T24" target="_self" title="LATTICE8:th.24">Th24</a></i>;<br/>
<a NAME="E39:47"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">d</font> <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"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c1">A</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E40:47"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c16">xo</font>,<font color="Maroon" title="c17">yo</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">d</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E41:47"/><b>then </b><i><font color="Green" title="E59">A24</font></i>: 
<font color="Maroon" title="c15">cd</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c16">xo</font>,<font color="Maroon" title="c17">yo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">d</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c8">y</font>
 
<b>by </b><i><a class="txt" href="lattice8.html#E38:47"><i><font color="Green" title="E58">A23</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E42:47"/>
 <a href="lattice8.html#K1" title="LATTICE8:func.1">new_set2</a> <font color="Maroon" title="c13">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice8.html#K3" title="LATTICE8:func.3">ConsecutiveSet2</a> <font color="Maroon" title="c1">A</font>,<span class="p1">(<span class="default"><a href="lattice5.html#K8" title="LATTICE5:func.8">DistEsti</a> <font color="Maroon" title="c3">d</font></span>)</span>
 
<b>by </b><i><a class="txt" href="lattice8.html#E23:47"><i><font color="Green" title="E45">A10</font></i></a>, <a class="txt" href="lattice8.html#E25:47"><i><font color="Green" title="E46">A11</font></i></a>, <a class="ref" href="lattice8.html#T22" target="_self" title="LATTICE8:th.22">Th22</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c20">z1</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>, <font color="Maroon" title="c21">z2</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">Aq</font> <b>by </b><i><a class="txt" href="lattice8.html#E3:47"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="lattice8.html#E29:47"><i><font color="Green" title="E49">A14</font></i></a>, <a class="txt" href="lattice8.html#E32:47"><i><font color="Green" title="E52">A17</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c20">z1</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c21">z2</font>
;<br/>

<b>thus </b><font color="Maroon" title="c5">dq</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c20">z1</font> = 
<span class="p1">(<span class="default"><a href="lattice8.html#K2" title="LATTICE8:func.2">new_bi_fun2</a> <font color="Maroon" title="c15">cd</font>,<font color="Maroon" title="c14">Q</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c18">x1</font>,<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="txt" href="lattice8.html#E4:47"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="lattice8.html#E26:47"><i><font color="Green" title="E47">A12</font></i></a>, <a class="txt" href="lattice8.html#E27:47"><i><font color="Green" title="E48">A13</font></i></a>, <a class="txt" href="lattice8.html#E35:47"><i><font color="Green" title="E55">A20</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">cd</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c16">xo</font>,<font color="Maroon" title="c16">xo</font></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c9">a</font>
<b>by </b><i><a class="txt" href="lattice8.html#E12:47"><i><font color="Green" title="E41">A6</font></i></a>, <a class="txt" href="lattice8.html#E14:47"><i><font color="Green" title="E43">A8</font></i></a>, <a class="ref" href="lattice8.html#D5" target="_self" title="LATTICE8:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c2">L</font></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c9">a</font>
<b>by </b><i><a class="txt" href="lattice8.html#E33:47"><i><font color="Green" title="E53">A18</font></i></a>, <a class="ref" href="lattice5.html#D7" title="LATTICE5:def.7">LATTICE5:def 7</a></i>
<br/>.= 
<font color="Maroon" title="c9">a</font>
<b>by </b><i><a class="ref" href="waybel_1.html#T4" title="WAYBEL_1:th.4">WAYBEL_1:4</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c5">dq</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c20">z1</font>,<font color="Maroon" title="c21">z2</font> = 
<span class="p1">(<span class="default"><a href="lattice8.html#K2" title="LATTICE8:func.2">new_bi_fun2</a> <font color="Maroon" title="c15">cd</font>,<font color="Maroon" title="c14">Q</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="txt" href="lattice8.html#E4:47"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="lattice8.html#E26:47"><i><font color="Green" title="E47">A12</font></i></a>, <a class="txt" href="lattice8.html#E27:47"><i><font color="Green" title="E48">A13</font></i></a>, <a class="txt" href="lattice8.html#E36:47"><i><font color="Green" title="E56">A21</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">d</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c8">y</font></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c10">b</font>
<b>by </b><i><a class="txt" href="lattice8.html#E12:47"><i><font color="Green" title="E41">A6</font></i></a>, <a class="txt" href="lattice8.html#E13:47"><i><font color="Green" title="E42">A7</font></i></a>, <a class="txt" href="lattice8.html#E14:47"><i><font color="Green" title="E43">A8</font></i></a>, <a class="txt" href="lattice8.html#E15:47"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="lattice8.html#E41:47"><i><font color="Green" title="E59">A24</font></i></a>, <a class="ref" href="lattice8.html#D5" target="_self" title="LATTICE8:def.5">Def5</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c5">dq</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c21">z2</font>,<font color="Maroon" title="c8">y</font> = 
<span class="p1">(<span class="default"><a href="lattice8.html#K2" title="LATTICE8:func.2">new_bi_fun2</a> <font color="Maroon" title="c15">cd</font>,<font color="Maroon" title="c14">Q</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c13">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c19">y1</font>
<b>by </b><i><a class="txt" href="lattice8.html#E4:47"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="lattice8.html#E26:47"><i><font color="Green" title="E47">A12</font></i></a>, <a class="txt" href="lattice8.html#E27:47"><i><font color="Green" title="E48">A13</font></i></a>, <a class="txt" href="lattice8.html#E37:47"><i><font color="Green" title="E57">A22</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">cd</font> <a href="lattice5.html#K4" title="LATTICE5:func.4">.</a> <font color="Maroon" title="c17">yo</font>,<font color="Maroon" title="c17">yo</font></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c9">a</font>
<b>by </b><i><a class="txt" href="lattice8.html#E13:47"><i><font color="Green" title="E42">A7</font></i></a>, <a class="txt" href="lattice8.html#E14:47"><i><font color="Green" title="E43">A8</font></i></a>, <a class="ref" href="lattice8.html#D5" target="_self" title="LATTICE8:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c2">L</font></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c9">a</font>
<b>by </b><i><a class="txt" href="lattice8.html#E33:47"><i><font color="Green" title="E53">A18</font></i></a>, <a class="ref" href="lattice5.html#D7" title="LATTICE5:def.7">LATTICE5:def 7</a></i>
<br/>.= 
<font color="Maroon" title="c9">a</font>
<b>by </b><i><a class="ref" href="waybel_1.html#T4" title="WAYBEL_1:th.4">WAYBEL_1:4</a></i>
;<br/>


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