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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be  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> ; <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">r</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><br/> for <font color="Olive" title="b2">H</font> being  <a href="seqfunc.html#NM1" title="SEQFUNC:NM.1">Functional_Sequence</a> of <font color="Maroon" title="c1">D</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <br/> for <font color="Olive" title="b3">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">H</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Olive" title="b3">X</font> holds <br/>( <font color="Olive" title="b1">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Olive" title="b2">H</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Olive" title="b3">X</font> &amp;  <a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Olive" title="b2">H</font></span>)</span>,<font color="Olive" title="b3">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b1">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Olive" title="b2">H</font>,<font color="Olive" title="b3">X</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</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">H</font> being  <a href="seqfunc.html#NM1" title="SEQFUNC:NM.1">Functional_Sequence</a> of <font color="Maroon" title="c1">D</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <br/> for <font color="Olive" title="b2">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">H</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Olive" title="b2">X</font> holds <br/>( <font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Olive" title="b1">H</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Olive" title="b2">X</font> &amp;  <a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Olive" title="b1">H</font></span>)</span>,<font color="Olive" title="b2">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Olive" title="b1">H</font>,<font color="Olive" title="b2">X</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">H</font> be   <a href="seqfunc.html#NM1" title="SEQFUNC:NM.1">Functional_Sequence</a> of <font color="Maroon" title="c1">D</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</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">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c3">H</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Olive" title="b1">X</font> holds <br/>( <font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Olive" title="b1">X</font> &amp;  <a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font></span>)</span>,<font color="Olive" title="b1">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Olive" title="b1">X</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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="c3">H</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Maroon" title="c4">X</font> implies ( <font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Maroon" title="c4">X</font> &amp;  <a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font></span>)</span>,<font color="Maroon" title="c4">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:56"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
<font color="Maroon" title="c3">H</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Maroon" title="c4">X</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">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Maroon" title="c4">X</font> &amp;  <a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font></span>)</span>,<font color="Maroon" title="c4">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span> )</span><br/>

<a NAME="E2:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A2</font></span>: 
<font color="Maroon" title="c4">X</font> <a href="seqfunc.html#R1" title="SEQFUNC:pred.1">common_on_dom</a> <font color="Maroon" title="c3">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="seqfunc.html#T21" target="_self" title="SEQFUNC:th.21">Th21</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E38">A3</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</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="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p2">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p2">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Maroon" title="c5">x</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:56_1"/><span class="lab"><font color="Green" title="E39">A4</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p2">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p2">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Maroon" title="c5">x</font></span>)</span></span><br/><a NAME="E2:56_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A5</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/><a NAME="E3:56_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A6</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="seqfunc.html#D14" target="_self" title="SEQFUNC:def.14">Def14</a></span>;<br/><a NAME="E4:56_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A7</font></span>: 
<font color="Maroon" title="c3">H</font> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Maroon" title="c5">x</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="seqfunc.html#T21" target="_self" title="SEQFUNC:th.21">Th21</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p2">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">x</font> = 
<font color="Maroon" title="c2">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_1"><span class="lab"><font color="Green" title="E39">A4</font></span></a>, <a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c2">r</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E2:56_1"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="ref" href="seqfunc.html#D14" target="_self" title="SEQFUNC:def.14">Def14</a></span>
<br/>.= 
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Maroon" title="c5">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:56_1"><span class="lab"><font color="Green" title="E42">A7</font></span></a>, <a class="ref" href="seq_2.html#T22" title="SEQ_2:th.22">SEQ_2:22</a></span>
<br/>.= 
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Maroon" title="c5">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E3:56_1"><span class="lab"><font color="Green" title="E41">A6</font></span></a>, <a class="ref" href="seqfunc.html#T34" target="_self" title="SEQFUNC:th.34">Th34</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>
<div><span class="lab"><font color="Green" title="E39">A8</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="56_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</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="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Maroon" title="c5">x</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:56_2"/><span class="lab"><font color="Green" title="E40">A9</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Maroon" title="c5">x</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> </span><br/><a NAME="E2:56_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">H</font> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Maroon" title="c5">x</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="seqfunc.html#T21" target="_self" title="SEQFUNC:th.21">Th21</a></span>;<br/><a NAME="E3:56_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Maroon" title="c5">x</font></span>)</span> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="seq_2.html#T21" title="SEQ_2:th.21">SEQ_2:21</a></span>;<br/><span class="kw">hence </span><a NAME="E4:56_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Maroon" title="c5">x</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E1:56_2"><span class="lab"><font color="Green" title="E40">A9</font></span></a>, <a class="ref" href="seqfunc.html#T34" target="_self" title="SEQFUNC:th.34">Th34</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>
<a NAME="E5:56"/>
<font color="Maroon" title="c4">X</font> <a href="seqfunc.html#R1" title="SEQFUNC:pred.1">common_on_dom</a> <font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="ref" href="seqfunc.html#T40" target="_self" title="SEQFUNC:th.40">Th40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:56"/><span class="lab"><font color="Green" title="E40">A10</font></span>: 
<font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font> <a href="seqfunc.html#R2" title="SEQFUNC:pred.2">is_point_conv_on</a> <font color="Maroon" title="c4">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E39">A8</font></span></a>, <a class="ref" href="seqfunc.html#T21" target="_self" title="SEQFUNC:th.21">Th21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font></span>)</span>,<font color="Maroon" title="c4">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span></span><br/>

 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p2">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span></span>)</span> = 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c4">X</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="seqfunc.html#D14" target="_self" title="SEQFUNC:def.14">Def14</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:56"/>
 <a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="seqfunc.html#K2" title="SEQFUNC:func.2">(#)</a> <font color="Maroon" title="c3">H</font></span>)</span>,<font color="Maroon" title="c4">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p1">(<span class="default"><a href="seqfunc.html#K11" title="SEQFUNC:func.11">lim</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c4">X</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:56"><span class="lab"><font color="Green" title="E40">A10</font></span></a>, <a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="ref" href="seqfunc.html#D14" target="_self" title="SEQFUNC:def.14">Def14</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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