<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">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">a</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <br/> for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</a>  holds <br/><font color="Olive" title="b1">a</font> <a href="rvsum_1.html#K11" title="RVSUM_1:func.11">*</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</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"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</a>  holds <br/><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K11" title="RVSUM_1:func.11">*</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</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">p</font>,<font color="Maroon" title="c4">q</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</a>  implies <font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K11" title="RVSUM_1:func.11">*</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</a>  )</span><br/>







<span class="kw">assume </span><a NAME="E1:181"/>
<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</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="c2">a</font> <a href="rvsum_1.html#K11" title="RVSUM_1:func.11">*</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</a> </span><br/>

<a NAME="E2:181"/><span class="kw">then </span>
<span class="p1"><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">|(</a><span class="default"><font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font></span><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#D18" target="_self" title="RVSUM_1:def.18">Def3</a></span>;<br/>
<a NAME="E3:181"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1"><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">|(</a><span class="default"><font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font></span><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<a NAME="E4:181"/><span class="kw">then </span>
<span class="p1"><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K11" title="RVSUM_1:func.11">*</a> <font color="Maroon" title="c3">p</font></span>)</span>,<font color="Maroon" title="c4">q</font></span><a href="rvsum_1.html#K23" title="RVSUM_1:func.23">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T161" target="_self" title="RVSUM_1:th.161">Th41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:181"/>
<font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K11" title="RVSUM_1:func.11">*</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font> <a href="rvsum_1.html#R1" title="RVSUM_1:pred.1">are_orthogonal</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#D18" target="_self" title="RVSUM_1:def.18">Def3</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/>


</div>
