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<b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>, <font color="Maroon">g</font> be   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:7_1_2"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><a href="complex2.html#K2">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Olive">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><a href="complex2.html#K2">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Olive">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<font color="Maroon">a</font></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>and </b><br/><a NAME="E2:7_1_2"/><i><font color="Green">E63</font></i>: 
for <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> holds  <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><a href="complex2.html#K2">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Olive">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><a href="complex2.html#K2">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Olive">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<font color="Maroon">a</font></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>thus </b><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> = 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3">Re</a> <span class="p3">(<span class="default"><a href="complex2.html#K2">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<font color="Maroon">a</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="complex1.html#K4">Im</a> <span class="p3">(<span class="default"><a href="complex2.html#K2">Rotate</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <a href="xcmplx_0.html#K1">&lt;i&gt;</a> </span>)</span></span>)</span>,<font color="Maroon">a</font></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:7_1_2"/>
<font color="Maroon">f</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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