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<span class="kw">let </span><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</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">N</font> being  <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>  st <font color="Olive" title="b2">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  holds <br/><font color="Olive" title="b2">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Olive" title="b1">N</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">N</font> be   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">S</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">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>  st <font color="Olive" title="b1">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  holds <br/><font color="Olive" title="b1">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span></span><br/>



<a NAME="E1:28"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">T</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</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="c4">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  implies <font color="Maroon" title="c4">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:28"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c4">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</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="c4">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</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="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E3:28"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <font color="Maroon" title="c3">N</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="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">p</font> = <font color="Maroon" title="c5">p</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">T</font> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E6:28"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>
 <span class="kw">and </span><br/><a NAME="E7:28"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <font color="Maroon" title="c3">N</font>
 <span class="kw">and </span><br/><a NAME="E8:28"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="funct_2.html#T115" title="FUNCT_2:th.115">FUNCT_2:115</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">x</font> = <font color="Maroon" title="c7">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E18">A4</font></span></a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">V</font> be    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c6">p</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="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font> <a href="waybel_0.html#R1" title="WAYBEL_0:pred.1">is_eventually_in</a> <font color="Maroon" title="c9">V</font></span><br/><a NAME="E1:28_1"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c9">V</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="connsp_2.html#D1" title="CONNSP_2:def.1">CONNSP_2:def 1</a></span>;<br/><a NAME="E2:28_1"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c9">V</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tops_1.html#T51" title="TOPS_1:th.51">TOPS_1:51</a></span>;<br/><a NAME="E3:28_1"/><span class="lab"><font color="Green" title="E23">A9</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c9">V</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E1:28_1"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="funct_2.html#T46" title="FUNCT_2:th.46">FUNCT_2:46</a></span>;<br/><a NAME="E4:28_1"/>
<font color="Maroon" title="c4">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c9">V</font></span>)</span> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E2:28_1"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="tops_2.html#T55" title="TOPS_2:th.55">TOPS_2:55</a></span>;<br/><a NAME="E5:28_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c9">V</font></span>)</span> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28_1"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="ref" href="connsp_2.html#T5" title="CONNSP_2:th.5">CONNSP_2:5</a></span>;<br/><a NAME="E6:28_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">N</font> <a href="waybel_0.html#R1" title="WAYBEL_0:pred.1">is_eventually_in</a> <font color="Maroon" title="c4">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c9">V</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="ref" href="yellow_6.html#D18" title="YELLOW_6:def.18">YELLOW_6:def 18</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">i</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font><span class="kw"> such that </span><br/><a NAME="E8:28_1"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
for <font color="Olive" title="b1">j</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font>  st <font color="Olive" title="b1">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c10">i</font> holds <br/><font color="Maroon" title="c3">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c9">V</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#D11" title="WAYBEL_0:def.11">WAYBEL_0:def 11</a></span>;<br/><a NAME="E9:28_1"/><span class="lab"><font color="Green" title="E25">A11</font></span>: 
the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c3">N</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_9.html#D8" title="WAYBEL_9:def.8">WAYBEL_9:def 8</a></span>;<br/><a NAME="E10:28_1"/><span class="lab"><font color="Green" title="E26">A12</font></span>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">N</font> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_9.html#D8" title="WAYBEL_9:def.8">WAYBEL_9:def 8</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">i9</font> = <font color="Maroon" title="c10">i</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span> ;<br/><span class="kw">thus </span><a NAME="E12:28_1"/>
<font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font> <a href="waybel_0.html#R1" title="WAYBEL_0:pred.1">is_eventually_in</a> <font color="Maroon" title="c9">V</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">take </span>
<font color="Maroon" title="c11">i9</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="waybel_0.html#D11" title="WAYBEL_0:def.11">WAYBEL_0:def 11</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">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span>  holds <br/>(  not <font color="Maroon" title="c11">i9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> or <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">V</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c12">j9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span>; <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="c11">i9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c12">j9</font> or <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c12">j9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">V</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c13">j</font> = <font color="Maroon" title="c12">j9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:28_1"><span class="lab"><font color="Green" title="E26">A12</font></span></a></span>;<br/>
<a NAME="E2:28_1_1"/><span class="lab"><font color="Green" title="E27">A13</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c13">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c12">j9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:28_1"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:28_1_1"/>
<font color="Maroon" title="c12">j9</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c11">i9</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="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c12">j9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">V</font></span><br/>

<a NAME="E4:28_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c13">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c9">V</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:28_1"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E10:28_1"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="yellow_0.html#T1" title="YELLOW_0:th.1">YELLOW_0:1</a></span>;<br/>
<a NAME="E5:28_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A14</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c13">j</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c9">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T46" title="FUNCT_2:th.46">FUNCT_2:46</a></span>;<br/>
<a NAME="E6:28_1_1"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c9">V</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tops_1.html#T44" title="TOPS_1:th.44">TOPS_1:44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:28_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c12">j9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">V</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28_1_1"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E5:28_1_1"><span class="lab"><font color="Green" title="E28">A14</font></span></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="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E11:28"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K10" title="YELLOW_6:func.10">Lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c3">N</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_6.html#D18" title="YELLOW_6:def.18">YELLOW_6:def 18</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>
