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<b>let </b><font color="Maroon" title="c3">y1</font>, <font color="Maroon" title="c4">y2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:5_1_1"/><i><font color="Green" title="E6">A2</font></i>: 
for <font color="Olive" title="b1">e1</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">e1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 holds <br/> ex <font color="Olive" title="b2">Y0</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( not <font color="Olive" title="b2">Y0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Olive" title="b2">Y0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> &amp; ( for <font color="Olive" title="b3">Y1</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b2">Y0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">Y1</font> &amp; <font color="Olive" title="b3">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> holds <br/><span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <font color="Olive" title="b3">Y1</font></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b1">e1</font> ) )
 <b>and </b><br/><a NAME="E2:5_1_1"/><i><font color="Green" title="E7">A3</font></i>: 
for <font color="Olive" title="b1">e2</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">e2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 holds <br/> ex <font color="Olive" title="b2">Y0</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( not <font color="Olive" title="b2">Y0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Olive" title="b2">Y0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> &amp; ( for <font color="Olive" title="b3">Y1</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b2">Y0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">Y1</font> &amp; <font color="Olive" title="b3">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> holds <br/><span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <font color="Olive" title="b3">Y1</font></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b1">e2</font> ) )
 ;<br/>

<div><i><font color="Green" title="E8">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">e3</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>assume </b><a NAME="E1:5_1_1_1"/><i><font color="Green" title="E9">A5</font></i>: 
<font color="Maroon" title="c5">e3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/><b>set </b><font color="Maroon" title="c6">e4</font> = <font color="Maroon" title="c5">e3</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2;<br/><a NAME="E2:5_1_1_1"/><i><font color="Green" title="E10">A6</font></i>: 
( <font color="Maroon" title="c5">e3</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2 is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> &amp; <font color="Maroon" title="c5">e3</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="bhsp_6.html#E1:5_1_1_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="real_2.html#T127" title="REAL_2:th.127">REAL_2:127</a></i>;<br/><a NAME="E3:5_1_1_1"/><i><font color="Green" title="E11">A7</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">e3</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2</span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">e3</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">e3</font>
 ;<br/><b>consider </b><font color="Maroon" title="c7">Y01</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E5:5_1_1_1"/><i><font color="Green" title="E12">A8</font></i>: 
( not <font color="Maroon" title="c7">Y01</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c7">Y01</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> &amp; ( for <font color="Olive" title="b1">Y1</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c7">Y01</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Y1</font> &amp; <font color="Olive" title="b1">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> holds <br/><span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <font color="Olive" title="b1">Y1</font></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">e3</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2 ) )
 <b>by </b><i><a class="txt" href="bhsp_6.html#E1:5_1_1"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="bhsp_6.html#E2:5_1_1_1"><i><font color="Green" title="E10">A6</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c8">Y02</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E7:5_1_1_1"/><i><font color="Green" title="E13">A9</font></i>: 
( not <font color="Maroon" title="c8">Y02</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c8">Y02</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> &amp; ( for <font color="Olive" title="b1">Y1</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c8">Y02</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Y1</font> &amp; <font color="Olive" title="b1">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> holds <br/><span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <font color="Olive" title="b1">Y1</font></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">e3</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2 ) )
 <b>by </b><i><a class="txt" href="bhsp_6.html#E2:5_1_1"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="bhsp_6.html#E2:5_1_1_1"><i><font color="Green" title="E10">A6</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c9">Y00</font> = <font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font>;<br/><a NAME="E8:5_1_1_1"/><i><font color="Green" title="E14">A10</font></i>: 
<font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E5:5_1_1_1"><i><font color="Green" title="E12">A8</font></i></a>, <a class="txt" href="bhsp_6.html#E7:5_1_1_1"><i><font color="Green" title="E13">A9</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/><a NAME="E9:5_1_1_1"/>
( <font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c7">Y01</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><a NAME="E10:5_1_1_1"/><b>then </b><i><font color="Green" title="E15">A11</font></i>: 
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">e3</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2
 <b>by </b><i><a class="txt" href="bhsp_6.html#E5:5_1_1_1"><i><font color="Green" title="E12">A8</font></i></a>, <a class="txt" href="bhsp_6.html#E8:5_1_1_1"><i><font color="Green" title="E14">A10</font></i></a></i>;<br/><a NAME="E11:5_1_1_1"/>
( <font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c8">Y02</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><a NAME="E12:5_1_1_1"/><b>then </b>
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">e3</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2
 <b>by </b><i><a class="txt" href="bhsp_6.html#E7:5_1_1_1"><i><font color="Green" title="E13">A9</font></i></a>, <a class="txt" href="bhsp_6.html#E8:5_1_1_1"><i><font color="Green" title="E14">A10</font></i></a></i>;<br/><a NAME="E13:5_1_1_1"/><b>then </b>
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">e3</font> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2
 <b>by </b><i><a class="ref" href="bhsp_1.html#T37" title="BHSP_1:th.37">BHSP_1:37</a></i>;<br/><a NAME="E14:5_1_1_1"/><b>then </b><i><font color="Green" title="E16">A12</font></i>: 
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">e3</font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E3:5_1_1_1"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="bhsp_6.html#E10:5_1_1_1"><i><font color="Green" title="E15">A11</font></i></a>, <a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><a NAME="E15:5_1_1_1"/>
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span>
 <b>by </b><i><a class="ref" href="bhsp_1.html#T36" title="BHSP_1:th.36">BHSP_1:36</a></i>;<br/><a NAME="E16:5_1_1_1"/><b>then </b>
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><span class="p2"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <font color="Maroon" title="c5">e3</font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E14:5_1_1_1"><i><font color="Green" title="E16">A12</font></i></a>, <a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><a NAME="E17:5_1_1_1"/><b>then </b><i><font color="Green" title="E17">A13</font></i>: 
<span class="p1">(<span class="default"><span class="p2"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p4">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p3"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><a href="binop_2.html#K7" title="BINOP_2:func.7">-</a> <span class="p2">(<span class="default"><span class="p3"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p3"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">e3</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p3"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><a href="binop_2.html#K7" title="BINOP_2:func.7">-</a> <span class="p2">(<span class="default"><span class="p3"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p3"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">y2</font></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> = 
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">y2</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>
<br/>.= 
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">y2</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></i>
<br/>.= 
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">y2</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
<br/>.= 
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T43" title="RLVECT_1:th.43">RLVECT_1:43</a></i>
<br/>.= 
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T41" title="RLVECT_1:th.41">RLVECT_1:41</a></i>
<br/>.= 
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T41" title="RLVECT_1:th.41">RLVECT_1:41</a></i>
<br/>.= 
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">y2</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><a href="bhsp_6.html#K1" title="BHSP_6:func.1">setsum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">Y01</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">Y02</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span>

;<br/><b>hence </b><a NAME="E19:5_1_1_1"/>
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">y2</font></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c5">e3</font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E17:5_1_1_1"><i><font color="Green" title="E17">A13</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:5_1_1"/>
<font color="Maroon" title="c3">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_1_1_2"/>
<font color="Maroon" title="c3">y1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">y2</font>
 ;<br/>

<a NAME="E2:5_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">y2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#T66" title="VECTSP_1:th.66">VECTSP_1:66</a></i>;<br/>
<a NAME="E3:5_1_1_2"/><b>then </b><i><font color="Green" title="E9">A14</font></i>: 
<span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">y2</font></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="bhsp_1.html#T32" title="BHSP_1:th.32">BHSP_1:32</a></i>;<br/>
<a NAME="E4:5_1_1_2"/>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="bhsp_1.html#K3" title="BHSP_1:func.3">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y1</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">y2</font></span>)</span></span><a href="bhsp_1.html#K3" title="BHSP_1:func.3">.||</a></span>
 
<b>by </b><i><a class="ref" href="bhsp_1.html#T34" title="BHSP_1:th.34">BHSP_1:34</a></i>;<br/>
<b>hence </b><a NAME="E5:5_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="bhsp_6.html#E3:5_1_1"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="bhsp_6.html#E3:5_1_1_2"><i><font color="Green" title="E9">A14</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:5_1_1"/>
<font color="Maroon" title="c3">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font>
 ;<br/>


</div>
