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<b>let </b><font color="Maroon" title="c1">s1</font>, <font color="Maroon" title="c2">s2</font>, <font color="Maroon" title="c3">t1</font>, <font color="Maroon" title="c4">t2</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:34"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>and </b><br/><a NAME="E2:34"/><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c2">s2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<a NAME="E3:34"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2
 
<b>by </b><i><a class="ref" href="euclid.html#T25" title="EUCLID:th.25">EUCLID:25</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">f</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2</span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">p</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>;<br/><a NAME="E1:34_1"/>
<font color="Maroon" title="c6">p</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="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>
 ;<br/><a NAME="E2:34_1"/><b>then </b><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c6">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2
 <b>by </b><i><a class="ref" href="euclid.html#T25" title="EUCLID:th.25">EUCLID:25</a></i>;<br/><b>set </b><font color="Maroon" title="c7">q</font> = <span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>;<br/><a NAME="E3:34_1"/><i><font color="Green" title="E30">A4</font></i>: 
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span>
 <b>by </b><i><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></i>;<br/><a NAME="E4:34_1"/><i><font color="Green" title="E31">A5</font></i>: 
<font color="Maroon" title="c1">s1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="jordan1k.html#E1:34"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="xcmplx_1.html#T107" title="XCMPLX_1:th.107">XCMPLX_1:107</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jgraph_2.html#K2" title="JGRAPH_2:func.2">AffineMap</a> <font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c4">t2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="jgraph_2.html#K2" title="JGRAPH_2:func.2">AffineMap</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>,<span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span>,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">p</font> = 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2" title="JGRAPH_2:func.2">AffineMap</a> <font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c4">t2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jgraph_2.html#K2" title="JGRAPH_2:func.2">AffineMap</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>,<span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span>,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">p</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T70" title="FUNCT_2:th.70">FUNCT_2:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2" title="JGRAPH_2:func.2">AffineMap</a> <font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c4">t2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>
<b>by </b><i><a class="ref" href="jgraph_2.html#D2" title="JGRAPH_2:def.2">JGRAPH_2:def 2</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">t1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">t2</font></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>
<b>by </b><i><a class="ref" href="jgraph_2.html#D2" title="JGRAPH_2:def.2">JGRAPH_2:def 2</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">t1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">t2</font></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>
<b>by </b><i><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">s1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">t1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">t2</font></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>

<br/>.= 
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c3">t1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c3">t1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">t2</font></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>
<b>by </b><i><a class="txt" href="jordan1k.html#E1:34"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="jordan1k.html#E4:34_1"><i><font color="Green" title="E31">A5</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">t2</font></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>
<b>by </b><i><a class="txt" href="jordan1k.html#E3:34_1"><i><font color="Green" title="E30">A4</font></i></a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">s2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c4">t2</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">t2</font></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>
<b>by </b><i><a class="txt" href="jordan1k.html#E2:34"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>
<br/>.= 
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c4">t2</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c4">t2</font></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>
<b>by </b><i><a class="txt" href="jordan1k.html#E2:34"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="xcmplx_1.html#T107" title="XCMPLX_1:th.107">XCMPLX_1:107</a></i>
<br/>.= 
<font color="Maroon" title="c6">p</font>
<b>by </b><i><a class="ref" href="euclid.html#T57" title="EUCLID:th.57">EUCLID:57</a></i>
<br/>.= 
<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">p</font>
<b>by </b><i><a class="txt" href="jordan1k.html#E2:34_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:34"/>
<span class="p1">(<span class="default"><a href="jgraph_2.html#K2" title="JGRAPH_2:func.2">AffineMap</a> <font color="Maroon" title="c1">s1</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c2">s2</font>,<font color="Maroon" title="c4">t2</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="jgraph_2.html#K2" title="JGRAPH_2:func.2">AffineMap</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">t1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">s1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">t2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c2">s2</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2</span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


</div>
