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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</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"> ( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">b</font> implies (  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  &amp; <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="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) &amp;  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  &amp; <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) ) )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">L</font> =  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c4">P</font> =  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>);<br/>
<span class="kw">assume </span><a NAME="E1:20"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">b</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="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  &amp; <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="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) &amp;  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  &amp; <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) )</span><br/>

<a NAME="E2:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A2</font></span>: 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</span> <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="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="treal_1.html#T15" target="_self" onmouseover="rs('treal_1/T15')" onmouseout="rh()">Th15</a></span>;<br/>
<a NAME="E3:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A3</font></span>: 
 <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T23" onmouseover="rs('funct_2/T23')" onmouseout="rh()">FUNCT_2:23</a></span>;<br/>
<a NAME="E4:20"/><span class="lab"><font color="Green" title="E19">A4</font></span>: 
(  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp;  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) 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="c1">a</font>,<font color="Maroon" title="c2">b</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="txt" href="#E1:20"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="treal_1.html#T8" target="_self" onmouseover="rs('treal_1/T8')" onmouseout="rh()">Th8</a>, <a class="ref" href="treal_1.html#T12" target="_self" onmouseover="rs('treal_1/T12')" onmouseout="rh()">Th12</a></span>;<br/>
<span class="lab"><font color="Green" title="E20">A5</font></span>:  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span> = 
 <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>

<br/>.= 
<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="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="treal_1.html#T15" target="_self" onmouseover="rs('treal_1/T15')" onmouseout="rh()">Th15</a></span>
;<br/>
<a NAME="E6:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A6</font></span>: 
 <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T23" onmouseover="rs('funct_2/T23')" onmouseout="rh()">FUNCT_2:23</a></span>;<br/>
<a NAME="E7:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A7</font></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="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></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="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>
 
;<br/>
<a NAME="E8:20"/><span class="lab"><font color="Green" title="E23">A8</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="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.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="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="ref" href="tops_2.html#D4" onmouseover="rs('tops_2/D4')" onmouseout="rh()">TOPS_2:def 4</a></span>;<br/>
<a NAME="E9:20"/>
(  <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="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></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> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span> &amp;  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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> <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="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="ref" href="funct_2.html#T30" onmouseover="rs('funct_2/T30')" onmouseout="rh()">FUNCT_2:30</a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:20"/>
 <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></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="txt" href="#E3:20"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="ref" href="tops_2.html#D5" onmouseover="rs('tops_2/D5')" onmouseout="rh()">TOPS_2:def 5</a></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"> ( <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="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) &amp;  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  &amp; <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) )</span><br/>

<span class="kw">thus </span><a NAME="E11:20"/>
<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="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p2">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="ref" href="funct_2.html#T30" onmouseover="rs('funct_2/T30')" onmouseout="rh()">FUNCT_2:30</a></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"> (  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  &amp; <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) )</span><br/>

<a NAME="E12:20"/><span class="lab"><font color="Green" title="E24">A9</font></span>: 
 <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="funct_2.html#T23" onmouseover="rs('funct_2/T23')" onmouseout="rh()">FUNCT_2:23</a></span>;<br/>
<a NAME="E13:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A10</font></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#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</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> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>
 
;<br/>
<a NAME="E14:20"/><span class="lab"><font color="Green" title="E26">A11</font></span>: 
(  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) 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> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span>,<span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span> &amp;  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) 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="#E1:20"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="treal_1.html#T8" target="_self" onmouseover="rs('treal_1/T8')" onmouseout="rh()">Th8</a>, <a class="ref" href="treal_1.html#T12" target="_self" onmouseover="rs('treal_1/T12')" onmouseout="rh()">Th12</a></span>;<br/>
<a NAME="E15:20"/><span class="lab"><font color="Green" title="E27">A12</font></span>: 
 <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="ref" href="funct_2.html#T23" onmouseover="rs('funct_2/T23')" onmouseout="rh()">FUNCT_2:23</a></span>;<br/>
<a NAME="E16:20"/><span class="lab"><font color="Green" title="E28">A13</font></span>: 
<span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:20"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="txt" href="#E12:20"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="ref" href="tops_2.html#D4" onmouseover="rs('tops_2/D4')" onmouseout="rh()">TOPS_2:def 4</a></span>;<br/>
<a NAME="E17:20"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</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="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span> &amp;  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:20"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="txt" href="#E15:20"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="ref" href="funct_2.html#T30" onmouseover="rs('funct_2/T30')" onmouseout="rh()">FUNCT_2:30</a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:20"/>
 <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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>,<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>) 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="#E13:20"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="txt" href="#E15:20"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="txt" href="#E16:20"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E14:20"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="ref" href="tops_2.html#D5" onmouseover="rs('tops_2/D5')" onmouseout="rh()">TOPS_2:def 5</a></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"> <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)</span><br/>

<span class="kw">thus </span><a NAME="E19:20"/>
<span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<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 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>)</span> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> (<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>,<span class="p1">(<span class="default">(<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>) <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:20"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="txt" href="#E15:20"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="txt" href="#E16:20"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="ref" href="funct_2.html#T30" onmouseover="rs('funct_2/T30')" onmouseout="rh()">FUNCT_2:30</a></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"> verum</span><br/>


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