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<span class="kw">let </span><font color="Maroon" title="c1">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <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>, <font color="Olive" title="b2">p2</font>, <font color="Olive" title="b3">q1</font>, <font color="Olive" title="b4">q2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>  st <font color="Maroon" title="c1">P</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font> &amp;  <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Olive" title="b3">q1</font>,<font color="Olive" title="b4">q2</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font> holds <br/> <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Olive" title="b4">q2</font>,<font color="Olive" title="b3">q1</font>,<font color="Maroon" title="c1">P</font>,<font color="Olive" title="b2">p2</font>,<font color="Olive" title="b1">p1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p1</font>, <font color="Maroon" title="c3">p2</font>, <font color="Maroon" title="c4">q1</font>, <font color="Maroon" title="c5">q2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <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="c1">P</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</font> &amp;  <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</font> implies  <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p1</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:19"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
<font color="Maroon" title="c1">P</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</font>
 <span class="kw">and </span><br/><a NAME="E2:19"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
 <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">p1</font>,<font color="Maroon" title="c3">p2</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">  <a href="jordan5c.html#R1" title="JORDAN5C:pred.1">LE</a> <font color="Maroon" title="c5">q2</font>,<font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c3">p2</font>,<font color="Maroon" title="c2">p1</font></span><br/>

<span class="kw">thus </span><a NAME="E3:19"/>
( <font color="Maroon" title="c5">q2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">P</font> &amp; <font color="Maroon" title="c4">q1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">P</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19"><span class="lab"><font color="Green" title="E18">A2</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="jordan5c.html#D3" onmouseover="rs('jordan5c/D3')" onmouseout="rh()">JORDAN5C:def 3</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">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">K16</a>(<a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">K17</a>( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c1">P</font></span>)</span>))<br/>  for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  or  not <font color="Olive">b<sub>1</sub></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="c3">p2</font> or  not <font color="Olive">b<sub>1</sub></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="c2">p1</font> or  not <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font> or  not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> or  not <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 or  not <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font> or  not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive">b<sub>3</sub></font> or  not <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 or <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive">b<sub>3</sub></font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">P9</font> = <font color="Maroon" title="c1">P</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="topreal1.html#T1" onmouseover="rs('topreal1/T1')" onmouseout="rh()">TOPREAL1:1</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="borsuk_1.html#K17" title="BORSUK_1:func.17">I[01]</a>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c1">P</font></span>)</span>; <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">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   holds <br/>(  not <font color="Maroon" title="c7">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  or  not <font color="Maroon" title="c7">f</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="c3">p2</font> or  not <font color="Maroon" title="c7">f</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="c2">p1</font> or  not <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font> or  not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> or  not <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 or  not <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font> or  not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> or  not <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 or <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">s1</font>, <font color="Maroon" title="c9">s2</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"> (  not <font color="Maroon" title="c7">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  or  not <font color="Maroon" title="c7">f</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="c3">p2</font> or  not <font color="Maroon" title="c7">f</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="c2">p1</font> or  not <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font> or  not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">s1</font> or  not <font color="Maroon" title="c8">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 or  not <font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font> or  not  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">s2</font> or  not <font color="Maroon" title="c9">s2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 or <font color="Maroon" title="c8">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">s2</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E5:19"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
<font color="Maroon" title="c7">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> 
 <span class="kw">and </span><br/><a NAME="E6:19"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
<font color="Maroon" title="c7">f</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="c3">p2</font>
 <span class="kw">and </span><br/><a NAME="E7:19"/><span class="lab"><font color="Green" title="E21">A5</font></span>: 
<font color="Maroon" title="c7">f</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="c2">p1</font>
 <span class="kw">and </span><br/><a NAME="E8:19"/><span class="lab"><font color="Green" title="E22">A6</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font>
 <span class="kw">and </span><br/><a NAME="E9:19"/><span class="lab"><font color="Green" title="E23">A7</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">s1</font>
 <span class="kw">and </span><br/><a NAME="E10:19"/><span class="lab"><font color="Green" title="E24">A8</font></span>: 
<font color="Maroon" title="c8">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <span class="kw">and </span><br/><a NAME="E11:19"/><span class="lab"><font color="Green" title="E25">A9</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font>
 <span class="kw">and </span><br/><a NAME="E12:19"/><span class="lab"><font color="Green" title="E26">A10</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">s2</font>
 <span class="kw">and </span><br/><a NAME="E13:19"/><span class="lab"><font color="Green" title="E27">A11</font></span>: 
<font color="Maroon" title="c9">s2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 ; <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="c8">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">s2</font></span><br/>

<a NAME="E14:19"/><span class="lab"><font color="Green" title="E28">A12</font></span>: 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c8">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:19"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="ref" href="xreal_1.html#T13" onmouseover="rs('xreal_1/T13')" onmouseout="rh()">XREAL_1:13</a></span>;<br/>
<a NAME="E15:19"/><span class="lab"><font color="Green" title="E29">A13</font></span>: 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:19"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="xreal_1.html#T13" onmouseover="rs('xreal_1/T13')" onmouseout="rh()">XREAL_1:13</a></span>;<br/>
<a NAME="E16:19"/><span class="lab"><font color="Green" title="E30">A14</font></span>: 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c8">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:19"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="ref" href="xreal_1.html#T13" onmouseover="rs('xreal_1/T13')" onmouseout="rh()">XREAL_1:13</a></span>;<br/>
<a NAME="E17:19"/><span class="lab"><font color="Green" title="E31">A15</font></span>: 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:19"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="xreal_1.html#T13" onmouseover="rs('xreal_1/T13')" onmouseout="rh()">XREAL_1:13</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">Ex</font> =  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>);<br/>
<a NAME="E18:19"/><span class="lab"><font color="Green" title="E32">A16</font></span>: 
 <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>) is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#T18" onmouseover="rs('treal_1/T18')" onmouseout="rh()">TREAL_1:18</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">g</font> = <font color="Maroon" title="c7">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p2">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>)</span>)</span>;<br/>
<a NAME="E19:19"/><span class="lab"><font color="Green" title="E33">A17</font></span>: 
<span class="p1">(<span class="default"><a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p2">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#D14" onmouseover="rs('borsuk_1/D14')" onmouseout="rh()">BORSUK_1:def 14</a>, <a class="ref" href="treal_1.html#T5" onmouseover="rs('treal_1/T5')" onmouseout="rh()">TREAL_1:5</a>, <a class="ref" href="treal_1.html#T9" onmouseover="rs('treal_1/T9')" onmouseout="rh()">TREAL_1:9</a></span>;<br/>
<a NAME="E20:19"/><span class="lab"><font color="Green" title="E34">A18</font></span>: 
<span class="p1">(<span class="default"><a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p2">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#D15" onmouseover="rs('borsuk_1/D15')" onmouseout="rh()">BORSUK_1:def 15</a>, <a class="ref" href="treal_1.html#T5" onmouseover="rs('treal_1/T5')" onmouseout="rh()">TREAL_1:5</a>, <a class="ref" href="treal_1.html#T9" onmouseover="rs('treal_1/T9')" onmouseout="rh()">TREAL_1:9</a></span>;<br/>
<a NAME="E21:19"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <a href="borsuk_1.html#K17" title="BORSUK_1:func.17">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="tops_2.html#D5" onmouseover="rs('tops_2/D5')" onmouseout="rh()">TOPS_2:def 5</a></span>;<br/>
<a NAME="E22:19"/><span class="kw">then </span>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p2">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<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> <font color="Maroon" title="c7">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:19"><span class="lab"><font color="Green" title="E32">A16</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#D5" onmouseover="rs('tops_2/D5')" onmouseout="rh()">TOPS_2:def 5</a></span>;<br/>
<a NAME="E23:19"/><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="c7">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p3">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p3">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>)</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="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p2">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>)</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="E24:19"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A19</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="c7">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p3">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p3">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>)</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> <a href="borsuk_1.html#K17" title="BORSUK_1:func.17">I[01]</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:19"><span class="lab"><font color="Green" title="E32">A16</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#D5" onmouseover="rs('tops_2/D5')" onmouseout="rh()">TOPS_2:def 5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">g</font> = <font color="Maroon" title="c7">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p2">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>)</span>)</span> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="borsuk_1.html#K17" title="BORSUK_1:func.17">I[01]</a>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c6">P9</font></span>)</span> <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="E26:19"/><span class="lab"><font color="Green" title="E36">A20</font></span>: 
<font color="Maroon" title="c12">g</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:19"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E18:19"><span class="lab"><font color="Green" title="E32">A16</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#T57" onmouseover="rs('tops_2/T57')" onmouseout="rh()">TOPS_2:57</a></span>;<br/>
<a NAME="E27:19"/><span class="lab"><font color="Green" title="E37">A21</font></span>: 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c8">s1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c12">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:19"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="txt" href="#E16:19"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E24:19"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/>
<a NAME="E28:19"/><span class="lab"><font color="Green" title="E38">A22</font></span>: 
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">s2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c12">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:19"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E17:19"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E24:19"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a></span>;<br/>
<a NAME="E29:19"/><span class="lab"><font color="Green" title="E39">A23</font></span>: 
<font color="Maroon" title="c12">g</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="c2">p1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:19"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E20:19"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E24:19"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="ref" href="borsuk_1.html#D14" onmouseover="rs('borsuk_1/D14')" onmouseout="rh()">BORSUK_1:def 14</a>, <a class="ref" href="funct_1.html#T12" onmouseover="rs('funct_1/T12')" onmouseout="rh()">FUNCT_1:12</a>, <a class="ref" href="treal_1.html#T5" onmouseover="rs('treal_1/T5')" onmouseout="rh()">TREAL_1:5</a></span>;<br/>
<a NAME="E30:19"/><span class="lab"><font color="Green" title="E40">A24</font></span>: 
<font color="Maroon" title="c12">g</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="c3">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E19:19"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E24:19"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="ref" href="borsuk_1.html#D15" onmouseover="rs('borsuk_1/D15')" onmouseout="rh()">BORSUK_1:def 15</a>, <a class="ref" href="funct_1.html#T12" onmouseover="rs('funct_1/T12')" onmouseout="rh()">FUNCT_1:12</a>, <a class="ref" href="treal_1.html#T5" onmouseover="rs('treal_1/T5')" onmouseout="rh()">TREAL_1:5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">qs1</font> = 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c8">s1</font>, <font color="Maroon" title="c14">qs2</font> = 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">s2</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:19"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="txt" href="#E15:19"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E16:19"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E17:19"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="ref" href="borsuk_1.html#T43" onmouseover="rs('borsuk_1/T43')" onmouseout="rh()">BORSUK_1:43</a>, <a class="ref" href="topmetr.html#T20" onmouseover="rs('topmetr/T20')" onmouseout="rh()">TOPMETR:20</a></span>;<br/>
<span class="lab"><font color="Green" title="E41">A25</font></span>: <span class="p1">(<span class="default"><a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p2">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">qs1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c8">s1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c8">s1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#D14" onmouseover="rs('borsuk_1/D14')" onmouseout="rh()">BORSUK_1:def 14</a>, <a class="ref" href="borsuk_1.html#D15" onmouseover="rs('borsuk_1/D15')" onmouseout="rh()">BORSUK_1:def 15</a>, <a class="ref" href="treal_1.html#T5" onmouseover="rs('treal_1/T5')" onmouseout="rh()">TREAL_1:5</a>, <a class="ref" href="treal_1.html#D3" onmouseover="rs('treal_1/D3')" onmouseout="rh()">TREAL_1:def 3</a></span>
<br/>.= 
<font color="Maroon" title="c8">s1</font>

;<br/>
<span class="lab"><font color="Green" title="E42">A26</font></span>: <span class="p1">(<span class="default"><a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p2">(<span class="default">(<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">qs2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">s2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">s2</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#D14" onmouseover="rs('borsuk_1/D14')" onmouseout="rh()">BORSUK_1:def 14</a>, <a class="ref" href="borsuk_1.html#D15" onmouseover="rs('borsuk_1/D15')" onmouseout="rh()">BORSUK_1:def 15</a>, <a class="ref" href="treal_1.html#T5" onmouseover="rs('treal_1/T5')" onmouseout="rh()">TREAL_1:5</a>, <a class="ref" href="treal_1.html#D3" onmouseover="rs('treal_1/D3')" onmouseout="rh()">TREAL_1:def 3</a></span>
<br/>.= 
<font color="Maroon" title="c9">s2</font>

;<br/>
<a NAME="E34:19"/><span class="lab"><font color="Green" title="E43">A27</font></span>: 
<font color="Maroon" title="c12">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c8">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:19"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E27:19"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E32:19"><span class="lab"><font color="Green" title="E41">A25</font></span></a>, <a class="ref" href="funct_1.html#T12" onmouseover="rs('funct_1/T12')" onmouseout="rh()">FUNCT_1:12</a></span>;<br/>
<a NAME="E35:19"/>
<font color="Maroon" title="c12">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">s2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E28:19"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="txt" href="#E33:19"><span class="lab"><font color="Green" title="E42">A26</font></span></a>, <a class="ref" href="funct_1.html#T12" onmouseover="rs('funct_1/T12')" onmouseout="rh()">FUNCT_1:12</a></span>;<br/>
<a NAME="E36:19"/><span class="kw">then </span>
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">s2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c8">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:19"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E14:19"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="txt" href="#E15:19"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E16:19"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E26:19"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="txt" href="#E29:19"><span class="lab"><font color="Green" title="E39">A23</font></span></a>, <a class="txt" href="#E30:19"><span class="lab"><font color="Green" title="E40">A24</font></span></a>, <a class="txt" href="#E34:19"><span class="lab"><font color="Green" title="E43">A27</font></span></a></span>;<br/>
<a NAME="E37:19"/><span class="kw">then </span>
<font color="Maroon" title="c8">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">s2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T11" onmouseover="rs('xreal_1/T11')" onmouseout="rh()">XREAL_1:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E38:19"/>
<font color="Maroon" title="c8">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">s2</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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