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<span class="kw">let </span><font color="Maroon" title="c1">f</font> be  non  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>   <a href="goboard5.html#V2" title="GOBOARD5:attr.2">standard</a>  <a href="goboard5.html#NM1" title="GOBOARD5:NM.1">special_circular_sequence</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">g</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> holds <br/> ( <font color="Olive" title="b1">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a> <font color="Maroon" title="c1">f</font> iff <font color="Olive" title="b1">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">g</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <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">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a> <font color="Maroon" title="c1">f</font> iff <font color="Maroon" title="c2">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> )</span><br/>



<a NAME="E1:74"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
 <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T67" title="SPRECT_1:th.67">SPRECT_1:67</a></span>;<br/>
<a NAME="E2:74"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
 <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T68" title="SPRECT_1:th.68">SPRECT_1:68</a></span>;<br/>
<a NAME="E3:74"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
 <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T69" title="SPRECT_1:th.69">SPRECT_1:69</a></span>;<br/>
<a NAME="E4:74"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
 <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sprect_1.html#T66" title="SPRECT_1:th.66">SPRECT_1:66</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:74"/>
( <font color="Maroon" title="c2">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a> <font color="Maroon" title="c1">f</font> implies <font color="Maroon" title="c2">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> )
  <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">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> implies <font color="Maroon" title="c2">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a> <font color="Maroon" title="c1">f</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:74_1"/><span class="lab"><font color="Green" title="E33">A5</font></span>: 
<font color="Maroon" title="c2">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a> <font color="Maroon" title="c1">f</font>
 ; <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">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="sprect_2.html#D1" title="SPRECT_2:def.1">SPRECT_2:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">g</font> or (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</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="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</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="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> ) )</span><br/>

<span class="kw">thus </span><a NAME="E2:74_1"/>
(  not <font color="Maroon" title="c3">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">g</font> or (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</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="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</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="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <span class="p2">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p3">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:74"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E3:74"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E1:74_1"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="ref" href="sprect_2.html#D1" title="SPRECT_2:def.1">SPRECT_2:def 1</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><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E6:74"/><span class="lab"><font color="Green" title="E33">A6</font></span>: 
<font color="Maroon" title="c2">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a>  <a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
 ; <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">g</font> <a href="sprect_2.html#R1" title="SPRECT_2:pred.1">is_in_the_area_of</a> <font color="Maroon" title="c1">f</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="sprect_2.html#D1" title="SPRECT_2:def.1">SPRECT_2:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">g</font> or (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></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="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></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="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> ) )</span><br/>

<span class="kw">thus </span><a NAME="E7:74"/>
(  not <font color="Maroon" title="c3">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">g</font> or (  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></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="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">E-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> &amp;  <a href="pscomp_1.html#K9" title="PSCOMP_1:func.9">S-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></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="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K7" title="PSCOMP_1:func.7">N-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:74"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E3:74"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E6:74"><span class="lab"><font color="Green" title="E33">A6</font></span></a>, <a class="ref" href="sprect_2.html#D1" title="SPRECT_2:def.1">SPRECT_2:def 1</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/>


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