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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">q</font> &amp; <font color="Maroon" title="c1">p</font> is <a href="valued_0.html#V7" title="VALUED_0:attr.7">increasing</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="valued_0.html#V7" title="VALUED_0:attr.7">increasing</a> implies <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font> )</span><br/>



<b>assume </b><a NAME="E1:7"/><i><font color="Green" title="E9">A1</font></i>: 
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c1">p</font> is <a href="valued_0.html#V7" title="VALUED_0:attr.7">increasing</a> or  not <font color="Maroon" title="c2">q</font> is <a href="valued_0.html#V7" title="VALUED_0:attr.7">increasing</a> or <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font> )</span><br/>

<b>assume </b><a NAME="E2:7"/><i><font color="Green" title="E10">A2</font></i>: 
( <font color="Maroon" title="c1">p</font> is <a href="valued_0.html#V7" title="VALUED_0:attr.7">increasing</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="valued_0.html#V7" title="VALUED_0:attr.7">increasing</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font></span><br/>

<a NAME="E3:7"/><b>then </b>
( <font color="Maroon" title="c1">p</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> )
 
<b>by </b><i><a class="ref" href="jordan7.html#T17" title="JORDAN7:th.17">JORDAN7:17</a></i>;<br/>
<a NAME="E4:7"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">q</font>
 
<b>by </b><i><a class="txt" href="#E1:7"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="finseq_1.html#T65" title="FINSEQ_1:th.65">FINSEQ_1:65</a></i>;<br/>
<b>hence </b><a NAME="E5:7"/>
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font>
 <b>by </b><i><a class="txt" href="#E1:7"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:7"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="goboard2.html#T22" title="GOBOARD2:th.22">GOBOARD2:22</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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