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<b>let </b><font color="Maroon" title="c1">R</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="algstr_0.html#L4" title="ALGSTR_0:struct.4">multLoopStr</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">A</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b2">L</font> being   <a href="ideal_1.html#M2" title="IDEAL_1:mode.2">LeftLinearCombination</a> of <font color="Olive" title="b1">A</font>  ex <font color="Olive" title="b3">E</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</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">R</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <font color="Olive" title="b3">E</font> <a href="ideal_1.html#R2" title="IDEAL_1:pred.2">represents</a> <font color="Olive" title="b2">L</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font>; <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">L</font> being   <a href="ideal_1.html#M2" title="IDEAL_1:mode.2">LeftLinearCombination</a> of <font color="Maroon" title="c2">A</font>  ex <font color="Olive" title="b2">E</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</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">R</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <font color="Olive" title="b2">E</font> <a href="ideal_1.html#R2" title="IDEAL_1:pred.2">represents</a> <font color="Olive" title="b1">L</font></span><br/><b>let </b><font color="Maroon" title="c3">L</font> be    <a href="ideal_1.html#M2" title="IDEAL_1:mode.2">LeftLinearCombination</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">E</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</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">R</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <font color="Olive" title="b1">E</font> <a href="ideal_1.html#R2" title="IDEAL_1:pred.2">represents</a> <font color="Maroon" title="c3">L</font></span><br/>





<b>set </b><font color="Maroon" title="c4">D</font> = <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">R</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<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> ] <b>means </b> ex <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> st <br/>( $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c3">L</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">y</font> );<br/>
<div><i><font color="Green" title="E34">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">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"> ( <font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">L</font></span>)</span> implies  ex <font color="Olive" title="b1">d</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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">R</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">k</font>,<font color="Olive" title="b1">d</font>] )</span><br/><b>assume </b><a NAME="E1:67_1"/>
<font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">L</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">d</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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">R</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">k</font>,<font color="Olive" title="b1">d</font>]</span><br/><a NAME="E2:67_1"/><b>then </b>
<font color="Maroon" title="c5">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>, <font color="Maroon" title="c7">a</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">A</font><b> such that </b><br/><a NAME="E4:67_1"/><i><font color="Green" title="E35">A2</font></i>: 
<font color="Maroon" title="c3">L</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c7">a</font>
 <b>by </b><i><a class="ref" href="ideal_1.html#D10" target="_self" title="IDEAL_1:def.10">Def10</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c8">b</font> = <font color="Maroon" title="c7">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> ;<br/><b>reconsider </b><font color="Maroon" title="c9">d</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c6">u</font>,<font color="Maroon" title="c8">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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">R</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> ;<br/><b>take </b><font color="Maroon" title="c10">d</font> = <font color="Maroon" title="c9">d</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">k</font>,<font color="Maroon" title="c10">d</font>]</span><br/><b>thus </b><a NAME="E7:67_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">k</font>,<font color="Maroon" title="c10">d</font>]
 <b>by </b><i><a class="txt" href="ideal_1.html#E4:67_1"><i><font color="Green" title="E35">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c5">E</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</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">R</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span><b> such that </b><br/><a NAME="E3:67"/><i><font color="Green" title="E35">A3</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">L</font></span>)</span>
 <b>and </b><br/><a NAME="E4:67"/><i><font color="Green" title="E36">A4</font></i>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">L</font></span>)</span> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>,<font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">k</font>]
 <b>from </b><i><a class="ref" href="polynom2.html#S1" title="POLYNOM2:sch.1">POLYNOM2:sch 1</a>(<a class="txt" href="ideal_1.html#E1:67"><i><font color="Green" title="E34">A1</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon" title="c5">E</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">E</font> <a href="ideal_1.html#R2" title="IDEAL_1:pred.2">represents</a> <font color="Maroon" title="c3">L</font></span><br/>

<a NAME="E5:67"/><i><font color="Green" title="E37">A5</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">L</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<b>thus </b><a NAME="E6:67"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">E</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="c3">L</font>
 <b>by </b><i><a class="txt" href="ideal_1.html#E3:67"><i><font color="Green" title="E35">A3</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ideal_1.html#D13" target="_self" title="IDEAL_1:def.13">IDEAL_1:def 13</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">i</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">L</font> holds <br/>( <font color="Maroon" title="c3">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> )</span><br/>

<b>let </b><font color="Maroon" title="c6">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">L</font> implies ( <font color="Maroon" title="c3">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> ) )</span><br/>

<b>assume </b><a NAME="E7:67"/><i><font color="Green" title="E38">A6</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> )</span><br/>

<b>reconsider </b><font color="Maroon" title="c7">k</font> = <font color="Maroon" title="c6">i</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="ideal_1.html#E7:67"><i><font color="Green" title="E38">A6</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">x</font>, <font color="Maroon" title="c9">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E10:67"/><i><font color="Green" title="E39">A7</font></i>: 
( <font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp; <font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c3">L</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c9">y</font> )
 <b>by </b><i><a class="txt" href="ideal_1.html#E4:67"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="ideal_1.html#E5:67"><i><font color="Green" title="E37">A5</font></i></a>, <a class="txt" href="ideal_1.html#E7:67"><i><font color="Green" title="E38">A6</font></i></a></i>;<br/>
<a NAME="E11:67"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y</font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E12:67"/>
<font color="Maroon" title="c3">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="ideal_1.html#E7:67"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="ideal_1.html#E10:67"><i><font color="Green" title="E39">A7</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font></span><br/>

<b>thus </b><a NAME="E13:67"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">E</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="ideal_1.html#E10:67"><i><font color="Green" title="E39">A7</font></i></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</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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