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<span class="kw">set </span><font color="Maroon" title="c1">X</font> =  the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">D</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<span class="kw">take </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is  <a href="ringcat1.html#V4" title="RINGCAT1:attr.4">Ring_DOMAIN-like</a>  &amp;  not <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )</span><br/>

<a NAME="E1:37_1_1"/>
 for <font color="Olive" title="b1">x</font> being    <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"> the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds  <font color="Olive" title="b1">x</font> is   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:37_1_1"/>
( <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is  <a href="ringcat1.html#V4" title="RINGCAT1:attr.4">Ring_DOMAIN-like</a>  &amp;  not <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ringcat1.html#D11" target="_self" title="RINGCAT1:def.11">Def12</a></span>; <a class="txt" 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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