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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</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">z1</font>, <font color="Olive" title="b2">z2</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Olive" title="b2">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K17" title="SEQ_4:func.17">0c</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Olive" title="b1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">z2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">z1</font>, <font color="Maroon" title="c3">z2</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font>; <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="c2">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c3">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K17" title="SEQ_4:func.17">0c</a> <font color="Maroon" title="c1">n</font> implies <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z2</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:107"/>
<font color="Maroon" title="c2">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c3">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K17" title="SEQ_4:func.17">0c</a> <font color="Maroon" title="c1">n</font>
 ; <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="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z2</font></span><br/>

<a NAME="E2:107"/><span class="kw">then </span>
<font color="Maroon" title="c2">z1</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <span class="p1">(<span class="default"><a href="seq_4.html#K18" title="SEQ_4:func.18">-</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K17" title="SEQ_4:func.17">0c</a> <font color="Maroon" title="c1">n</font>
 
;<br/>
<a NAME="E3:107"/><span class="kw">then </span>
<font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K18" title="SEQ_4:func.18">-</a> <span class="p1">(<span class="default"><a href="seq_4.html#K18" title="SEQ_4:func.18">-</a> <font color="Maroon" title="c3">z2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#T68" target="_self" title="SEQ_4:th.68">Th7</a>, <a class="ref" href="seq_4.html#T69" target="_self" title="SEQ_4:th.69">Th8</a>, <a class="ref" href="binop_2.html#T1" title="BINOP_2:th.1">BINOP_2:1</a>, <a class="ref" href="finseqop.html#T78" title="FINSEQOP:th.78">FINSEQOP:78</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:107"/>
<font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z2</font>
 ; <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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