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<span class="kw">let </span><font color="Maroon" title="c1">CNS</font> be   <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</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">RNS</font> being  <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/> for <font color="Olive" title="b2">f</font> being  <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Olive" title="b1">RNS</font>,<font color="Maroon" title="c1">CNS</font><br/> for <font color="Olive" title="b3">x0</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">RNS</font>  st <font color="Olive" title="b2">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Olive" title="b3">x0</font> holds <br/>( <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Olive" title="b2">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="nfcont_1.html#R2" title="NFCONT_1:pred.2">is_continuous_in</a> <font color="Olive" title="b3">x0</font> &amp;  <a href="vfunct_2.html#K6" title="VFUNCT_2:func.6">-</a> <font color="Olive" title="b2">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Olive" title="b3">x0</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">RNS</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</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">f</font> being  <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Maroon" title="c2">RNS</font>,<font color="Maroon" title="c1">CNS</font><br/> for <font color="Olive" title="b2">x0</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">RNS</font>  st <font color="Olive" title="b1">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Olive" title="b2">x0</font> holds <br/>( <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Olive" title="b1">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="nfcont_1.html#R2" title="NFCONT_1:pred.2">is_continuous_in</a> <font color="Olive" title="b2">x0</font> &amp;  <a href="vfunct_2.html#K6" title="VFUNCT_2:func.6">-</a> <font color="Olive" title="b1">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Olive" title="b2">x0</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Maroon" title="c2">RNS</font>,<font color="Maroon" title="c1">CNS</font>; <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">x0</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">RNS</font>  st <font color="Maroon" title="c3">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Olive" title="b1">x0</font> holds <br/>( <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="nfcont_1.html#R2" title="NFCONT_1:pred.2">is_continuous_in</a> <font color="Olive" title="b1">x0</font> &amp;  <a href="vfunct_2.html#K6" title="VFUNCT_2:func.6">-</a> <font color="Maroon" title="c3">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Olive" title="b1">x0</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">x0</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">RNS</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="c3">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Maroon" title="c4">x0</font> implies ( <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="nfcont_1.html#R2" title="NFCONT_1:pred.2">is_continuous_in</a> <font color="Maroon" title="c4">x0</font> &amp;  <a href="vfunct_2.html#K6" title="VFUNCT_2:func.6">-</a> <font color="Maroon" title="c3">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Maroon" title="c4">x0</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:73"/><span class="lab"><font color="Green" title="E43">A1</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Maroon" title="c4">x0</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"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="nfcont_1.html#R2" title="NFCONT_1:pred.2">is_continuous_in</a> <font color="Maroon" title="c4">x0</font> &amp;  <a href="vfunct_2.html#K6" title="VFUNCT_2:func.6">-</a> <font color="Maroon" title="c3">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Maroon" title="c4">x0</font> )</span><br/>

<a NAME="E2:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A2</font></span>: 
<font color="Maroon" title="c4">x0</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> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ncfcont1.html#D17" target="_self" title="NCFCONT1:def.17">Def17</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1"><span class="kw">now </span></a><div class="add"><span class="kw">thus </span><a NAME="E1:73_1"/><span class="lab"><font color="Green" title="E45">A3</font></span>: 
<font color="Maroon" title="c4">x0</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"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:73"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="ncfcont1.html#D4" target="_self" title="NCFCONT1:def.4">Def4</a></span>; <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">s1</font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c2">RNS</font>  st  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b1">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> &amp; <font color="Olive" title="b1">s1</font> is  <a href="normsp_1.html#V3" title="NORMSP_1:attr.3">convergent</a>  &amp;  <a href="normsp_1.html#K8" title="NORMSP_1:func.8">lim</a> <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x0</font> holds <br/>( <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Olive" title="b1">s1</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>  &amp; <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x0</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"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Olive" title="b1">s1</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">s1</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c2">RNS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c5">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> &amp; <font color="Maroon" title="c5">s1</font> is  <a href="normsp_1.html#V3" title="NORMSP_1:attr.3">convergent</a>  &amp;  <a href="normsp_1.html#K8" title="NORMSP_1:func.8">lim</a> <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x0</font> implies ( <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">s1</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>  &amp; <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x0</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"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">s1</font></span>)</span> ) )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:73_1"/><span class="lab"><font color="Green" title="E46">A4</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c5">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span>
 <span class="kw">and </span><br/><a NAME="E3:73_1"/><span class="lab"><font color="Green" title="E47">A5</font></span>: 
( <font color="Maroon" title="c5">s1</font> is  <a href="normsp_1.html#V3" title="NORMSP_1:attr.3">convergent</a>  &amp;  <a href="normsp_1.html#K8" title="NORMSP_1:func.8">lim</a> <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x0</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"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">s1</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>  &amp; <span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x0</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"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">s1</font></span>)</span> )</span><br/><a NAME="E4:73_1"/><span class="lab"><font color="Green" title="E48">A6</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c5">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:73_1"><span class="lab"><font color="Green" title="E46">A4</font></span></a>, <a class="ref" href="ncfcont1.html#D4" target="_self" title="NCFCONT1:def.4">Def4</a></span>;<br/><a NAME="E5:73_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A7</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="clvect_1.html#K9" title="CLVECT_1:func.9">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">s1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E3:73_1"><span class="lab"><font color="Green" title="E47">A5</font></span></a>, <a class="ref" href="ncfcont1.html#D17" target="_self" title="NCFCONT1:def.17">Def17</a></span>;<br/><a NAME="E6:73_1"/><span class="lab"><font color="Green" title="E50">A8</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">s1</font> is  <a href="clvect_1.html#V9" title="CLVECT_1:attr.9">convergent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E3:73_1"><span class="lab"><font color="Green" title="E47">A5</font></span></a>, <a class="txt" href="#E4:73_1"><span class="lab"><font color="Green" title="E48">A6</font></span></a>, <a class="ref" href="ncfcont1.html#D17" target="_self" title="NCFCONT1:def.17">Def17</a></span>;<br/><a NAME="E7:73_1"/><span class="kw">then </span>
<span class="p1"><a href="clvect_1.html#K8" title="CLVECT_1:func.8">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">s1</font></span>)</span></span><a href="clvect_1.html#K8" title="CLVECT_1:func.8">.||</a></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="clvect_1.html#T119" title="CLVECT_1:th.119">CLVECT_1:119</a></span>;<br/><span class="kw">hence </span><a NAME="E8:73_1"/>
<span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">s1</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="#E4:73_1"><span class="lab"><font color="Green" title="E48">A6</font></span></a>, <a class="ref" href="ncfcont1.html#T52" target="_self" title="NCFCONT1:th.52">Th52</a></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"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x0</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"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">s1</font></span>)</span></span><br/><span class="kw">thus </span><span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x0</font> = 
<span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">x0</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73_1"><span class="lab"><font color="Green" title="E45">A3</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1"><a href="clvect_1.html#K6" title="CLVECT_1:func.6">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">x0</font></span>)</span></span><a href="clvect_1.html#K6" title="CLVECT_1:func.6">.||</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73_1"><span class="lab"><font color="Green" title="E45">A3</font></span></a>, <a class="ref" href="ncfcont1.html#D4" target="_self" title="NCFCONT1:def.4">Def4</a></span>
<br/>.= 
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1"><a href="clvect_1.html#K8" title="CLVECT_1:func.8">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">s1</font></span>)</span></span><a href="clvect_1.html#K8" title="CLVECT_1:func.8">.||</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:73_1"><span class="lab"><font color="Green" title="E50">A8</font></span></a>, <a class="txt" href="#E5:73_1"><span class="lab"><font color="Green" title="E49">A7</font></span></a>, <a class="ref" href="clopban1.html#T45" title="CLOPBAN1:th.45">CLOPBAN1:45</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"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">s1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:73_1"><span class="lab"><font color="Green" title="E48">A6</font></span></a>, <a class="ref" href="ncfcont1.html#T52" target="_self" title="NCFCONT1:th.52">Th52</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">hence </span><a NAME="E4:73"/>
<span class="p1"><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">||.</a><span class="default"><font color="Maroon" title="c3">f</font></span><a href="ncfcont1.html#K3" title="NCFCONT1:func.3">.||</a></span> <a href="nfcont_1.html#R2" title="NFCONT_1:pred.2">is_continuous_in</a> <font color="Maroon" title="c4">x0</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nfcont_1.html#D10" title="NFCONT_1:def.10">NFCONT_1:def 10</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="vfunct_2.html#K6" title="VFUNCT_2:func.6">-</a> <font color="Maroon" title="c3">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Maroon" title="c4">x0</font></span><br/>

<a NAME="E5:73"/>
 <a href="vfunct_2.html#K6" title="VFUNCT_2:func.6">-</a> <font color="Maroon" title="c3">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="vfunct_2.html#K4" title="VFUNCT_2:func.4">(#)</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vfunct_2.html#T23" title="VFUNCT_2:th.23">VFUNCT_2:23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:73"/>
 <a href="vfunct_2.html#K6" title="VFUNCT_2:func.6">-</a> <font color="Maroon" title="c3">f</font> <a href="ncfcont1.html#R3" title="NCFCONT1:pred.3">is_continuous_in</a> <font color="Maroon" title="c4">x0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="ref" href="ncfcont1.html#T58" target="_self" title="NCFCONT1:th.58">Th58</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>
