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<b>consider </b><font color="Maroon" title="c1">a</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<b>reconsider </b><font color="Maroon" title="c2">z</font> =  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>take </b>
 <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c2">z</font> #)
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c2">z</font> #) is <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a> &amp;  <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c2">z</font> #) is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> &amp; not  <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c2">z</font> #) is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )</span><br/>

<b>thus </b><a NAME="E3:8_1_1"/>
(  <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c2">z</font> #) is <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a> &amp;  <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c2">z</font> #) is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> &amp; not  <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c2">z</font> #) is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 ; <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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