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<span class="kw">let </span><font color="Maroon" title="c1">f1</font>, <font color="Maroon" title="c2">f2</font>, <font color="Maroon" title="c3">f3</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.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">  for <font color="Olive" title="b1">t</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds  <span class="p1">(<span class="default"><a href="euclid_8.html#K6" title="EUCLID_8:func.6">VFunc</a> (<font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c3">f3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">t</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"> <span class="p1">(<span class="default"><a href="euclid_8.html#K6" title="EUCLID_8:func.6">VFunc</a> (<font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c3">f3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span></span><br/>







<a NAME="E1:64"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
( <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 
;<br/>
<a NAME="E2:64"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
( <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 
;<br/>
<a NAME="E3:64"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
( <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
;<br/>
<span class="lab"><font color="Green" title="E27">A4</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</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="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</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><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="euclid_8.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</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="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</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><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:64"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="euclid_8.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 1</span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:64"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="euclid_8.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>

;<br/>
<a NAME="E5:64"/><span class="lab"><font color="Green" title="E28">A5</font></span>: 
( <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <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="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font> &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 
;<br/>
<a NAME="E6:64"/><span class="lab"><font color="Green" title="E29">A6</font></span>: 
( <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font> &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 
;<br/>
<a NAME="E7:64"/><span class="lab"><font color="Green" title="E30">A7</font></span>: 
( <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font> )
 
;<br/>
<span class="lab"><font color="Green" title="E31">A8</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span> = 
<span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:64"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="txt" href="#E5:64"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E6:64"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="euclid_8.html#E3"><span class="lab"><font color="Green" title="E3">Lm2</font></span></a></span>
<br/>.= 
<span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>

;<br/>
<a NAME="E9:64"/>
( <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <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="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font> &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font> &amp; <span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 
;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span> = 
<span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:64"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E8:64"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="euclid_8.html#E3"><span class="lab"><font color="Green" title="E3">Lm2</font></span></a></span>
<br/>.= 
<span class="p1"><a href="euclid_8.html#K1" title="EUCLID_8:func.1">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span></span><a href="euclid_8.html#K1" title="EUCLID_8:func.1">]|</a></span>

;<br/>
<span class="kw">hence </span><a NAME="E11:64"/>
<span class="p1">(<span class="default"><a href="euclid_8.html#K6" title="EUCLID_8:func.6">VFunc</a> (<font color="Maroon" title="c1">f1</font>,<font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c3">f3</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K2" title="EUCLID_8:func.2">&lt;e1&gt;</a></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K3" title="EUCLID_8:func.3">&lt;e2&gt;</a></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <a href="euclid_8.html#K4" title="EUCLID_8:func.4">&lt;e3&gt;</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_8.html#D5" target="_self" onmouseover="rs('euclid_8/D5')" onmouseout="rh()">Def5</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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