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<b>let </b><font color="Maroon" title="c1">I</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> ; <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">J</font> being <a href="waybel_3.html#V4" title="WAYBEL_3:attr.4">non-Empty</a> <a href="waybel18.html#V1" title="WAYBEL18:attr.1">TopSpace-yielding</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b2">i1</font>, <font color="Olive" title="b3">i2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b4">xi1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Olive" title="b2">i1</font></span>)</span><br/> for <font color="Olive" title="b5">Ai2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Olive" title="b3">i2</font></span>)</span>  st <font color="Olive" title="b5">Ai2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Olive" title="b3">i2</font></span>)</span> holds <br/>( <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Olive" title="b1">J</font>,<font color="Olive" title="b2">i1</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b4">xi1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Olive" title="b1">J</font>,<font color="Olive" title="b3">i2</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Olive" title="b5">Ai2</font> iff ( <font color="Olive" title="b2">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">i2</font> &amp; <font color="Olive" title="b4">xi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b5">Ai2</font> ) )</span><br/><b>let </b><font color="Maroon" title="c2">J</font> be  <a href="waybel_3.html#V4" title="WAYBEL_3:attr.4">non-Empty</a> <a href="waybel18.html#V1" title="WAYBEL18:attr.1">TopSpace-yielding</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</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">i1</font>, <font color="Olive" title="b2">i2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b3">xi1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Olive" title="b1">i1</font></span>)</span><br/> for <font color="Olive" title="b4">Ai2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Olive" title="b2">i2</font></span>)</span>  st <font color="Olive" title="b4">Ai2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Olive" title="b2">i2</font></span>)</span> holds <br/>( <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Olive" title="b1">i1</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b3">xi1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Olive" title="b2">i2</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Olive" title="b4">Ai2</font> iff ( <font color="Olive" title="b1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">i2</font> &amp; <font color="Olive" title="b3">xi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">Ai2</font> ) )</span><br/><b>let </b><font color="Maroon" title="c3">i1</font>, <font color="Maroon" title="c4">i2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</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">xi1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Maroon" title="c3">i1</font></span>)</span><br/> for <font color="Olive" title="b2">Ai2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Maroon" title="c4">i2</font></span>)</span>  st <font color="Olive" title="b2">Ai2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Maroon" title="c4">i2</font></span>)</span> holds <br/>( <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Maroon" title="c3">i1</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">xi1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Maroon" title="c4">i2</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Olive" title="b2">Ai2</font> iff ( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font> &amp; <font color="Olive" title="b1">xi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">Ai2</font> ) )</span><br/><b>let </b><font color="Maroon" title="c5">xi1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Maroon" title="c3">i1</font></span>)</span>; <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">Ai2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Maroon" title="c4">i2</font></span>)</span>  st <font color="Olive" title="b1">Ai2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Maroon" title="c4">i2</font></span>)</span> holds <br/>( <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Maroon" title="c3">i1</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">xi1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Maroon" title="c4">i2</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Olive" title="b1">Ai2</font> iff ( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font> &amp; <font color="Maroon" title="c5">xi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Ai2</font> ) )</span><br/><b>let </b><font color="Maroon" title="c6">Ai2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Maroon" title="c4">i2</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">Ai2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Maroon" title="c4">i2</font></span>)</span> implies ( <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Maroon" title="c3">i1</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">xi1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Maroon" title="c4">i2</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c6">Ai2</font> iff ( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font> &amp; <font color="Maroon" title="c5">xi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Ai2</font> ) ) )</span><br/>









<a NAME="E1:14"/><i><font color="Green" title="E14">A1</font></i>: 
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">J</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<a NAME="E2:14"/>
<font color="Maroon" title="c3">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 
;<br/>
<a NAME="E3:14"/><b>then </b><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c3">i1</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> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E4:14"/>
<font color="Maroon" title="c4">i2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 
;<br/>
<a NAME="E5:14"/><b>then </b><i><font color="Green" title="E16">A3</font></i>: 
<font color="Maroon" title="c4">i2</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> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<b>assume </b><a NAME="E6:14"/><i><font color="Green" title="E17">A4</font></i>: 
<font color="Maroon" title="c6">Ai2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Maroon" title="c4">i2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Maroon" title="c3">i1</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">xi1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Maroon" title="c4">i2</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c6">Ai2</font> iff ( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font> &amp; <font color="Maroon" title="c5">xi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Ai2</font> ) )</span><br/>

<a NAME="E7:14"/>
<font color="Maroon" title="c5">xi1</font> <a href="hidden.html#R2" title="HIDDEN: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"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Maroon" title="c3">i1</font></span>)</span>
 
;<br/>
<a NAME="E8:14"/><b>then </b><i><font color="Green" title="E18">A5</font></i>: 
<font color="Maroon" title="c5">xi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i1</font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#T9" title="YELLOW_6:th.9">YELLOW_6:9</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">Ai2'</font> = <font color="Maroon" title="c6">Ai2</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i2</font></span>)</span> <b>by </b><i><a class="ref" href="yellow_6.html#T9" title="YELLOW_6:th.9">YELLOW_6:9</a></i>;<br/>
<a NAME="E10:14"/>
<font color="Maroon" title="c6">Ai2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">J</font> <a href="waybel18.html#K4" title="WAYBEL18:func.4">.</a> <font color="Maroon" title="c4">i2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E6:14"><i><font color="Green" title="E17">A4</font></i></a></i>;<br/>
<a NAME="E11:14"/><b>then </b>
<font color="Maroon" title="c7">Ai2'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i2</font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#T9" title="YELLOW_6:th.9">YELLOW_6:9</a></i>;<br/>
<a NAME="E12:14"/><b>then </b>
( <span class="p1">(<span class="default"><a href="pralg_3.html#K3" title="PRALG_3:func.3">proj</a> <span class="p2">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">J</font></span>)</span>,<font color="Maroon" title="c3">i1</font></span>)</span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">xi1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K3" title="PRALG_3:func.3">proj</a> <span class="p2">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">J</font></span>)</span>,<font color="Maroon" title="c4">i2</font></span>)</span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c7">Ai2'</font> iff ( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font> &amp; <font color="Maroon" title="c5">xi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">Ai2'</font> ) )
 
<b>by </b><i><a class="txt" href="#E1:14"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E3:14"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="#E5:14"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="#E8:14"><i><font color="Green" title="E18">A5</font></i></a>, <a class="ref" href="yellow17.html#T7" target="_self" title="YELLOW17:th.7">Th7</a></i>;<br/>
<a NAME="E13:14"/><b>then </b>
( <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Maroon" title="c3">i1</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">xi1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K3" title="PRALG_3:func.3">proj</a> <span class="p2">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</a> <font color="Maroon" title="c2">J</font></span>)</span>,<font color="Maroon" title="c4">i2</font></span>)</span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c6">Ai2</font> iff ( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font> &amp; <font color="Maroon" title="c5">xi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">Ai2'</font> ) )
 
<b>by </b><i><a class="ref" href="waybel18.html#D4" title="WAYBEL18:def.4">WAYBEL18:def 4</a></i>;<br/>
<b>hence </b><a NAME="E14:14"/>
( <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Maroon" title="c3">i1</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">xi1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel18.html#K6" title="WAYBEL18:func.6">proj</a> <font color="Maroon" title="c2">J</font>,<font color="Maroon" title="c4">i2</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <font color="Maroon" title="c6">Ai2</font> iff ( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font> &amp; <font color="Maroon" title="c5">xi1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Ai2</font> ) )
 <b>by </b><i><a class="ref" href="waybel18.html#D4" title="WAYBEL18:def.4">WAYBEL18:def 4</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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