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

<a NAME="E1:43_1_1"/>
 <a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">x</font> where <font color="Olive" title="b1">x</font> is   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font> : verum </span>}</span> 
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">ca</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">x</font> where <font color="Olive" title="b1">x</font> is   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font> : verum </span>}</span>  as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<div><i><font color="Green" title="E22">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>thus </b><a NAME="E1:43_1_1_1"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">ca</font> implies <font color="Maroon" title="c4">x</font> is   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_1_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">ca</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">y</font> being   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E3:43_1_1_1_1"/><i><font color="Green" title="E23">A2</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font>
 ;<br/>
<b>thus </b><a NAME="E4:43_1_1_1_1"/>
<font color="Maroon" title="c4">x</font> is   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font>
 <b>by </b><i><a class="txt" href="hahnban1.html#E3:43_1_1_1_1"><i><font color="Green" title="E23">A2</font></i></a></i>;<br/>


</div><b>end;</b></div><b>thus </b><a NAME="E2:43_1_1_1"/>
( <font color="Maroon" title="c4">x</font> is   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font> implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">ca</font> )
 ;<br/></div><b>end;</b></div>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="hahnban1.html#NM1" title="HAHNBAN1:NM.1">Functional</a> of <font color="Maroon" title="c2">V</font> st <br/>( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> &amp; $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> &amp; $3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</a> <font color="Olive" title="b2">g</font> );<br/>
<a NAME="E4:43_1_1"/><i><font color="Green" title="E23">A3</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font>  ex <font color="Olive" title="b3">u</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">u</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c6">f</font> = <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c7">g</font> = <font color="Maroon" title="c5">y</font> as   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="txt" href="hahnban1.html#E3:43_1_1"><i><font color="Green" title="E22">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">u</font> = <font color="Maroon" title="c6">f</font> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</a> <font color="Maroon" title="c7">g</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font> <b>by </b><i><a class="txt" href="hahnban1.html#E3:43_1_1"><i><font color="Green" title="E22">A1</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c8">u</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c6">f</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c7">g</font>
;<br/>

<b>thus </b><a NAME="E3:43_1_1_2"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font> &amp; <font color="Maroon" title="c8">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</a> <font color="Maroon" title="c7">g</font> )
 ;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c4">ad</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">ca</font>,<font color="Maroon" title="c3">ca</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c3">ca</font><b> such that </b><br/><a NAME="E6:43_1_1"/><i><font color="Green" title="E24">A4</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Maroon" title="c4">ad</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>]
 <b>from </b><i><a class="ref" href="binop_1.html#S3" title="BINOP_1:sch.3">BINOP_1:sch 3</a>(<a class="txt" href="hahnban1.html#E4:43_1_1"><i><font color="Green" title="E23">A3</font></i></a>);<br/></i>
<div><i><font color="Green" title="E25">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">f</font>, <font color="Maroon" title="c6">g</font> be   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font>;<br/><b>reconsider </b><font color="Maroon" title="c7">x</font> = <font color="Maroon" title="c5">f</font>, <font color="Maroon" title="c8">y</font> = <font color="Maroon" title="c6">g</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font> <b>by </b><i><a class="txt" href="hahnban1.html#E3:43_1_1"><i><font color="Green" title="E22">A1</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c9">f1</font>, <font color="Maroon" title="c10">g1</font> being   <a href="hahnban1.html#NM1" title="HAHNBAN1:NM.1">Functional</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E3:43_1_1_3"/><i><font color="Green" title="E26">A6</font></i>: 
( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f1</font> &amp; <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">g1</font> &amp; <font color="Maroon" title="c4">ad</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f1</font> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</a> <font color="Maroon" title="c10">g1</font> )
 <b>by </b><i><a class="txt" href="hahnban1.html#E6:43_1_1"><i><font color="Green" title="E24">A4</font></i></a></i>;<br/><b>thus </b><a NAME="E4:43_1_1_3"/>
<font color="Maroon" title="c4">ad</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</a> <font color="Maroon" title="c6">g</font>
 <b>by </b><i><a class="txt" href="hahnban1.html#E3:43_1_1_3"><i><font color="Green" title="E26">A6</font></i></a></i>;<br/></div><b>end;</b></div>
<b>reconsider </b><font color="Maroon" title="c5">0F</font> =  <a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font> <b>by </b><i><a class="txt" href="hahnban1.html#E3:43_1_1"><i><font color="Green" title="E22">A1</font></i></a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">f</font> being  <a href="hahnban1.html#NM1" title="HAHNBAN1:NM.1">Functional</a> of <font color="Maroon" title="c2">V</font> st <br/>( $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> &amp; $3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <font color="Olive" title="b1">f</font> );<br/>
<a NAME="E9:43_1_1"/><i><font color="Green" title="E26">A7</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b2">y</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font>  ex <font color="Olive" title="b3">u</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font> st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">u</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c7">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font>;<br/>



<b>reconsider </b><font color="Maroon" title="c8">f</font> = <font color="Maroon" title="c7">y</font> as   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="txt" href="hahnban1.html#E3:43_1_1"><i><font color="Green" title="E22">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">u</font> = <font color="Maroon" title="c6">x</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <font color="Maroon" title="c8">f</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font> <b>by </b><i><a class="txt" href="hahnban1.html#E3:43_1_1"><i><font color="Green" title="E22">A1</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c9">u</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c8">f</font>
;<br/>

<b>thus </b><a NAME="E3:43_1_1_4"/>
( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font> &amp; <font color="Maroon" title="c9">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <font color="Maroon" title="c8">f</font> )
 ;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c6">lm</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c3">ca</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c3">ca</font><b> such that </b><br/><a NAME="E11:43_1_1"/><i><font color="Green" title="E27">A8</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b2">y</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font> holds  <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Maroon" title="c6">lm</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>]
 <b>from </b><i><a class="ref" href="binop_1.html#S3" title="BINOP_1:sch.3">BINOP_1:sch 3</a>(<a class="txt" href="hahnban1.html#E9:43_1_1"><i><font color="Green" title="E26">A7</font></i></a>);<br/></i>
<div><i><font color="Green" title="E28">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">f</font> be   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c8">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>;<br/><b>reconsider </b><font color="Maroon" title="c9">y</font> = <font color="Maroon" title="c7">f</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">ca</font> <b>by </b><i><a class="txt" href="hahnban1.html#E3:43_1_1"><i><font color="Green" title="E22">A1</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c10">f1</font> being   <a href="hahnban1.html#NM1" title="HAHNBAN1:NM.1">Functional</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E3:43_1_1_5"/><i><font color="Green" title="E29">A10</font></i>: 
( <font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f1</font> &amp; <font color="Maroon" title="c6">lm</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <font color="Maroon" title="c10">f1</font> )
 <b>by </b><i><a class="txt" href="hahnban1.html#E11:43_1_1"><i><font color="Green" title="E27">A8</font></i></a></i>;<br/><b>thus </b><a NAME="E4:43_1_1_5"/>
<font color="Maroon" title="c6">lm</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <font color="Maroon" title="c7">f</font>
 <b>by </b><i><a class="txt" href="hahnban1.html#E3:43_1_1_5"><i><font color="Green" title="E29">A10</font></i></a></i>;<br/></div><b>end;</b></div>
<b>reconsider </b><font color="Maroon" title="c7">V1</font> =  <a href="vectsp_1.html#G4" title="VECTSP_1:aggr.4">VectSpStr</a>(# <font color="Maroon" title="c3">ca</font>,<font color="Maroon" title="c4">ad</font>,<font color="Maroon" title="c5">0F</font>,<font color="Maroon" title="c6">lm</font> #) as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="vectsp_1.html#V11" title="VECTSP_1:attr.11">strict</a>  <a href="vectsp_1.html#L4" title="VECTSP_1:struct.4">VectSpStr</a> of <font color="Maroon" title="c1">K</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c7">V1</font>
;<br/>

<b>thus </b><a NAME="E14:43_1_1"/>
( ( for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">V1</font> iff <font color="Olive" title="b1">x</font> is   <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font> ) ) &amp; ( for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font> holds  the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c7">V1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="hahnban1.html#K3" title="HAHNBAN1:func.3">+</a> <font color="Olive" title="b2">g</font> ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c7">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font> &amp; ( for <font color="Olive" title="b1">f</font> being  <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font><br/> for <font color="Olive" title="b2">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font> holds  the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <font color="Maroon" title="c7">V1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> <a href="hahnban1.html#K6" title="HAHNBAN1:func.6">*</a> <font color="Olive" title="b1">f</font> ) )
 <b>by </b><i><a class="txt" href="hahnban1.html#E3:43_1_1"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="hahnban1.html#E7:43_1_1"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="hahnban1.html#E12:43_1_1"><i><font color="Green" title="E28">A9</font></i></a></i>;<br/>


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