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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">r1</font>, <font color="Olive" title="b2">r2</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b3">t1</font>, <font color="Olive" title="b4">t2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b5">p1</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Olive" title="b3">t1</font>,<font color="Olive" title="b4">t2</font>  st <font color="Olive" title="b3">t1</font>,<font color="Olive" title="b4">t2</font> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">are_connected</a>  &amp; <font color="Olive" title="b1">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">r2</font> holds <br/><font color="Olive" title="b5">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Olive" title="b1">r1</font>,<font color="Olive" title="b2">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> is   <a href="topalg_6.html#V7" title="TOPALG_6:attr.7">with_endpoints</a>  <a href="topalg_6.html#NM1" title="TOPALG_6:NM.1">Curve</a> of <font color="Maroon" title="c1">T</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">r1</font>, <font color="Maroon" title="c3">r2</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t1</font>, <font color="Olive" title="b2">t2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b3">p1</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Olive" title="b1">t1</font>,<font color="Olive" title="b2">t2</font>  st <font color="Olive" title="b1">t1</font>,<font color="Olive" title="b2">t2</font> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c2">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">r2</font> holds <br/><font color="Olive" title="b3">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> is   <a href="topalg_6.html#V7" title="TOPALG_6:attr.7">with_endpoints</a>  <a href="topalg_6.html#NM1" title="TOPALG_6:NM.1">Curve</a> of <font color="Maroon" title="c1">T</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">t1</font>, <font color="Maroon" title="c5">t2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p1</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">t1</font>,<font color="Maroon" title="c5">t2</font>  st <font color="Maroon" title="c4">t1</font>,<font color="Maroon" title="c5">t2</font> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c2">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">r2</font> holds <br/><font color="Olive" title="b1">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> is   <a href="topalg_6.html#V7" title="TOPALG_6:attr.7">with_endpoints</a>  <a href="topalg_6.html#NM1" title="TOPALG_6:NM.1">Curve</a> of <font color="Maroon" title="c1">T</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">p1</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">t1</font>,<font color="Maroon" title="c5">t2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">t1</font>,<font color="Maroon" title="c5">t2</font> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c2">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">r2</font> implies <font color="Maroon" title="c6">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> is   <a href="topalg_6.html#V7" title="TOPALG_6:attr.7">with_endpoints</a>  <a href="topalg_6.html#NM1" title="TOPALG_6:NM.1">Curve</a> of <font color="Maroon" title="c1">T</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:61"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
<font color="Maroon" title="c4">t1</font>,<font color="Maroon" title="c5">t2</font> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">are_connected</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">r2</font> or <font color="Maroon" title="c6">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> is   <a href="topalg_6.html#V7" title="TOPALG_6:attr.7">with_endpoints</a>  <a href="topalg_6.html#NM1" title="TOPALG_6:NM.1">Curve</a> of <font color="Maroon" title="c1">T</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:61"/><span class="lab"><font color="Green" title="E36">A2</font></span>: 
<font color="Maroon" title="c2">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">r2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> is   <a href="topalg_6.html#V7" title="TOPALG_6:attr.7">with_endpoints</a>  <a href="topalg_6.html#NM1" title="TOPALG_6:NM.1">Curve</a> of <font color="Maroon" title="c1">T</font></span><br/>

<a NAME="E3:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A3</font></span>: 
 <a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) is   <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_6.html#T34" onmouseover="rs('borsuk_6/T34')" onmouseout="rh()">BORSUK_6:34</a></span>;<br/>
<a NAME="E4:61"/><span class="lab"><font color="Green" title="E38">A4</font></span>: 
( <font color="Maroon" title="c6">p1</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp; <font color="Maroon" title="c6">p1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t1</font> &amp; <font color="Maroon" title="c6">p1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">t2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="borsuk_2.html#D2" onmouseover="rs('borsuk_2/D2')" onmouseout="rh()">BORSUK_2:def 2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">c</font> = <font color="Maroon" title="c6">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>;<br/>
<a NAME="E5:61"/>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" onmouseover="rs('relat_1/D19')" onmouseout="rh()">RELAT_1:def 19</a></span>;<br/>
<a NAME="E6:61"/><span class="kw">then </span>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> <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="c6">p1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a>, <a class="ref" href="topmetr.html#T20" onmouseover="rs('topmetr/T20')" onmouseout="rh()">TOPMETR:20</a></span>;<br/>
<a NAME="E7:61"/><span class="kw">then </span>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T27" onmouseover="rs('relat_1/T27')" onmouseout="rh()">RELAT_1:27</a></span>;<br/>
<a NAME="E8:61"/><span class="kw">then </span>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E9:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A5</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:61"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="topmetr.html#T18" onmouseover="rs('topmetr/T18')" onmouseout="rh()">TOPMETR:18</a></span>;<br/>
<a NAME="E10:61"/><span class="lab"><font color="Green" title="E40">A6</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font>
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">c</font> = <font color="Maroon" title="c6">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> as   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a>,<font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:61"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="ref" href="relset_1.html#T4" onmouseover="rs('relset_1/T4')" onmouseout="rh()">RELSET_1:4</a>, <a class="ref" href="topmetr.html#T17" onmouseover="rs('topmetr/T17')" onmouseout="rh()">TOPMETR:17</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">S</font> = <a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c8">c</font></span>)</span>;<br/>
<a NAME="E12:61"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#D5" onmouseover="rs('pre_topc/D5')" onmouseout="rh()">PRE_TOPC:def 5</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">g</font> = <font color="Maroon" title="c8">c</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:61"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="ref" href="funct_2.html#T2" onmouseover="rs('funct_2/T2')" onmouseout="rh()">FUNCT_2:2</a></span>;<br/>
<a NAME="E14:61"/><span class="lab"><font color="Green" title="E41">A7</font></span>: 
<a href="topalg_2.html#K2" title="TOPALG_2:func.2">R^1</a> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:61"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E9:61"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="ref" href="topmetr.html#T19" onmouseover="rs('topmetr/T19')" onmouseout="rh()">TOPMETR:19</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">p2</font> = <font color="Maroon" title="c6">p1</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>,<font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#T20" onmouseover="rs('topmetr/T20')" onmouseout="rh()">TOPMETR:20</a></span>;<br/>
<a NAME="E16:61"/>
<font color="Maroon" title="c10">g</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:61"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E14:61"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="txt" href="#E3:61"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="ref" href="topmetr.html#T20" onmouseover="rs('topmetr/T20')" onmouseout="rh()">TOPMETR:20</a>, <a class="ref" href="tops_2.html#T46" onmouseover="rs('tops_2/T46')" onmouseout="rh()">TOPS_2:46</a></span>;<br/>
<a NAME="E17:61"/><span class="kw">then </span>
<font color="Maroon" title="c8">c</font> is  <a href="topalg_6.html#V4" title="TOPALG_6:attr.4">parametrized-curve</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:61"><span class="lab"><font color="Green" title="E39">A5</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">c</font> = <font color="Maroon" title="c8">c</font> as   <a href="topalg_6.html#NM1" title="TOPALG_6:NM.1">Curve</a> of <font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="topalg_6.html#T20" target="_self" onmouseover="rs('topalg_6/T20')" onmouseout="rh()">Th20</a></span>;<br/>
<a NAME="E19:61"/>
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c12">c</font> is  <a href="xxreal_2.html#V1" title="XXREAL_2:attr.1">left_end</a>  &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c12">c</font> is  <a href="xxreal_2.html#V2" title="XXREAL_2:attr.2">right_end</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:61"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E9:61"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="ref" href="xxreal_2.html#T33" onmouseover="rs('xxreal_2/T33')" onmouseout="rh()">XXREAL_2:33</a></span>;<br/>
<a NAME="E20:61"/><span class="kw">then </span>
( <font color="Maroon" title="c12">c</font> is  <a href="topalg_6.html#V5" title="TOPALG_6:attr.5">with_first_point</a>  &amp; <font color="Maroon" title="c12">c</font> is  <a href="topalg_6.html#V6" title="TOPALG_6:attr.6">with_last_point</a>  )
 
;<br/>
<span class="kw">hence </span><a NAME="E21:61"/>
<font color="Maroon" title="c6">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> (<font color="Maroon" title="c2">r1</font>,<font color="Maroon" title="c3">r2</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> is   <a href="topalg_6.html#V7" title="TOPALG_6:attr.7">with_endpoints</a>  <a href="topalg_6.html#NM1" title="TOPALG_6:NM.1">Curve</a> of <font color="Maroon" title="c1">T</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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