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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be  <a href="membered.html#V1" title="MEMBERED:attr.1">complex-membered</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">a</font> being <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Olive" title="b1">a</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">a</font> be  <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Maroon" title="c3">a</font></span>)</span> )</span><br/>





<b>assume </b><a NAME="E1:370"/><i><font color="Green" title="E153">A1</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <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"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Maroon" title="c3">a</font></span>)</span></span><br/>

<a NAME="E2:370"/><i><font color="Green" title="E154">A2</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="member_1.html#T43" target="_self" title="MEMBER_1:th.43">Th43</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Maroon" title="c3">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> </span>)</span> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">B</font></span>)</span>
<b>by </b><i><a class="ref" href="member_1.html#T43" target="_self" title="MEMBER_1:th.43">Th43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> </span>)</span> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> </span>)</span> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c2">B</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:370"><i><font color="Green" title="E153">A1</font></i></a>, <a class="ref" href="member_1.html#T204" target="_self" title="MEMBER_1:th.204">Th204</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K24" title="MEMBER_1:func.24">///</a> <font color="Maroon" title="c3">a</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:370"><i><font color="Green" title="E154">A2</font></i></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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