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<b>let </b><font color="Maroon" title="c12">f</font>, <font color="Maroon" title="c13">g</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c10">r</font></span>)</span>,<span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c10">r</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:99_1_2"/><i><font color="Green" title="E74">A8</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c10">r</font></span>)</span>  ex <font color="Olive" title="b2">y</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> <font color="Maroon" title="c7">n</font></span>)</span> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> &amp; <font color="Maroon" title="c12">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="brouwer.html#K3" title="BROUWER:func.3">HC</a> <font color="Olive" title="b2">y</font>,<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c10">r</font> )
 <b>and </b><br/><a NAME="E2:99_1_2"/><i><font color="Green" title="E75">A9</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c10">r</font></span>)</span>  ex <font color="Olive" title="b2">y</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> <font color="Maroon" title="c7">n</font></span>)</span> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> &amp; <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="brouwer.html#K3" title="BROUWER:func.3">HC</a> <font color="Olive" title="b2">y</font>,<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c10">r</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c14">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:99_1_2_1"/><i><font color="Green" title="E76">A10</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c10">r</font></span>)</span>
 ;<br/><a NAME="E2:99_1_2_1"/><i><font color="Green" title="E77">A11</font></i>: 
 ex <font color="Olive" title="b1">y</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> <font color="Maroon" title="c7">n</font></span>)</span> st <br/>( <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> &amp; <font color="Maroon" title="c12">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="brouwer.html#K3" title="BROUWER:func.3">HC</a> <font color="Olive" title="b1">y</font>,<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c10">r</font> )
 <b>by </b><i><a class="txt" href="jordan.html#E1:99_1_2"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="jordan.html#E1:99_1_2_1"><i><font color="Green" title="E76">A10</font></i></a></i>;<br/><a NAME="E3:99_1_2_1"/>
 ex <font color="Olive" title="b1">y</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> <font color="Maroon" title="c7">n</font></span>)</span> st <br/>( <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> &amp; <font color="Maroon" title="c13">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="brouwer.html#K3" title="BROUWER:func.3">HC</a> <font color="Olive" title="b1">y</font>,<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c10">r</font> )
 <b>by </b><i><a class="txt" href="jordan.html#E2:99_1_2"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="jordan.html#E1:99_1_2_1"><i><font color="Green" title="E76">A10</font></i></a></i>;<br/><b>hence </b><a NAME="E4:99_1_2_1"/>
<font color="Maroon" title="c12">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">x</font>
 <b>by </b><i><a class="txt" href="jordan.html#E2:99_1_2_1"><i><font color="Green" title="E77">A11</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:99_1_2"/>
<font color="Maroon" title="c12">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</a></i>;<br/>


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