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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K27" title="MEMBER_1:func.27">///</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#K27" title="MEMBER_1:func.27">///</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K27" title="MEMBER_1:func.27">///</a> <font color="Olive" title="b1">a</font></span>)</span></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K27" title="MEMBER_1:func.27">///</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#K27" title="MEMBER_1:func.27">///</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K27" title="MEMBER_1:func.27">///</a> <font color="Maroon" title="c3">a</font></span>)</span> )</span><br/>





<span class="kw">assume </span><a NAME="E1:364"/><span class="lab"><font color="Green" title="E146">A1</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K27" title="MEMBER_1:func.27">///</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#K27" title="MEMBER_1:func.27">///</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K27" title="MEMBER_1:func.27">///</a> <font color="Maroon" title="c3">a</font></span>)</span></span><br/>

<a NAME="E2:364"/><span class="lab"><font color="Green" title="E147">A2</font></span>: 
<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#K7" title="MEMBER_1:func.7">""</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="binop_2.html#K2" title="BINOP_2:func.2">"</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="member_1.html#T37" target="_self" title="MEMBER_1:th.37">Th37</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K27" title="MEMBER_1:func.27">///</a> <font color="Maroon" title="c3">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> </span>)</span> <a href="member_1.html#K23" title="MEMBER_1:func.23">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <font color="Maroon" title="c2">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="member_1.html#T37" target="_self" title="MEMBER_1:th.37">Th37</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> </span>)</span> <a href="member_1.html#K23" title="MEMBER_1:func.23">**</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> </span>)</span> <a href="member_1.html#K23" title="MEMBER_1:func.23">**</a> <font color="Maroon" title="c2">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:364"><span class="lab"><font color="Green" title="E146">A1</font></span></a>, <a class="ref" href="member_1.html#T200" target="_self" title="MEMBER_1:th.200">Th200</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K27" title="MEMBER_1:func.27">///</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K27" title="MEMBER_1:func.27">///</a> <font color="Maroon" title="c3">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:364"><span class="lab"><font color="Green" title="E147">A2</font></span></a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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