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<b>let </b><font color="Maroon" title="c1">seq</font>, <font color="Maroon" title="c2">seq1</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a> &amp; <font color="Maroon" title="c2">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> implies <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a> ) &amp; ( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a> &amp; <font color="Maroon" title="c2">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> implies <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a> ) &amp; ( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <font color="Maroon" title="c2">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> implies <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> ) )</span><br/>



<b>thus </b><a NAME="E1:88"/>
( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a> &amp; <font color="Maroon" title="c2">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> implies <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a> &amp; <font color="Maroon" title="c2">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> implies <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a> ) &amp; ( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <font color="Maroon" title="c2">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> implies <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="88_1"><b>proof </b></a><div class="add">

<b>assume </b><b>that </b><br/><a NAME="E1:88_1"/><i><font color="Green" title="E55">A1</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a>
 <b>and </b><br/><a NAME="E2:88_1"/><i><font color="Green" title="E56">A2</font></i>: 
<font color="Maroon" title="c2">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a></span><br/>

<a NAME="E3:88_1"/>
<font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 
<b>by </b><i><a class="txt" href="seqm_3.html#E2:88_1"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="seqm_3.html#T73" target="_self" title="SEQM_3:th.73">Th73</a></i>;<br/>
<a NAME="E4:88_1"/><b>then </b>
<font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a>
 
<b>by </b><i><a class="ref" href="seq_2.html#D5" title="SEQ_2:def.5">SEQ_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:88_1"/>
<font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a>
 <b>by </b><i><a class="txt" href="seqm_3.html#E1:88_1"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="seqm_3.html#T71" target="_self" title="SEQM_3:th.71">Th71</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>thus </b><a NAME="E2:88"/>
( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a> &amp; <font color="Maroon" title="c2">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> implies <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <font color="Maroon" title="c2">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> implies <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="88_2"><b>proof </b></a><div class="add">

<b>assume </b><b>that </b><br/><a NAME="E1:88_2"/><i><font color="Green" title="E55">A3</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a>
 <b>and </b><br/><a NAME="E2:88_2"/><i><font color="Green" title="E56">A4</font></i>: 
<font color="Maroon" title="c2">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a></span><br/>

<a NAME="E3:88_2"/>
<font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 
<b>by </b><i><a class="txt" href="seqm_3.html#E2:88_2"><i><font color="Green" title="E56">A4</font></i></a>, <a class="ref" href="seqm_3.html#T73" target="_self" title="SEQM_3:th.73">Th73</a></i>;<br/>
<a NAME="E4:88_2"/><b>then </b>
<font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a>
 
<b>by </b><i><a class="ref" href="seq_2.html#D5" title="SEQ_2:def.5">SEQ_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:88_2"/>
<font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a>
 <b>by </b><i><a class="txt" href="seqm_3.html#E1:88_2"><i><font color="Green" title="E55">A3</font></i></a>, <a class="ref" href="seqm_3.html#T71" target="_self" title="SEQM_3:th.71">Th71</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>assume </b><b>that </b><br/><a NAME="E3:88"/><i><font color="Green" title="E55">A5</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 <b>and </b><br/><a NAME="E4:88"/><i><font color="Green" title="E56">A6</font></i>: 
<font color="Maroon" title="c2">seq1</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a></span><br/>

<a NAME="E5:88"/>
<font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 
<b>by </b><i><a class="txt" href="seqm_3.html#E4:88"><i><font color="Green" title="E56">A6</font></i></a>, <a class="ref" href="seqm_3.html#T73" target="_self" title="SEQM_3:th.73">Th73</a></i>;<br/>
<b>hence </b><a NAME="E6:88"/>
<font color="Maroon" title="c1">seq</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">seq1</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 <b>by </b><i><a class="txt" href="seqm_3.html#E3:88"><i><font color="Green" title="E55">A5</font></i></a>, <a class="ref" href="seqm_3.html#T71" target="_self" title="SEQM_3:th.71">Th71</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>
