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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">seq</font> being  <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a><br/> for <font color="Olive" title="b2">h</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> , <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>   st <font color="Olive" title="b2">h</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> holds <br/><font color="Olive" title="b2">h</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">seq</font> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">h</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Olive" title="b1">seq</font></span>)</span> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">n</font></span><br/><b>let </b><font color="Maroon" title="c2">seq</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</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">h</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> , <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>   st <font color="Olive" title="b1">h</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> holds <br/><font color="Olive" title="b1">h</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">h</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">n</font></span><br/><b>let </b><font color="Maroon" title="c3">h</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> , <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</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">h</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> implies <font color="Maroon" title="c3">h</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">n</font> )</span><br/>





<b>assume </b><a NAME="E1:27"/>
<font color="Maroon" title="c3">h</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</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">h</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">n</font></span><br/>

<a NAME="E2:27"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 
<b>by </b><i><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></i>;<br/>
<a NAME="E3:27"/><b>then </b>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c2">seq</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font>
 
;<br/>
<b>hence </b><a NAME="E4:27"/>
<font color="Maroon" title="c3">h</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="comseq_3.html#K6" title="COMSEQ_3:func.6">^\</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="cfcont_1.html#T17" target="_self" title="CFCONT_1:th.17">Th17</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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