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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th20</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: FUNCSDOM:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b3">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>)  st <font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Olive" title="b1">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">x2</font> &amp; <font color="Olive" title="b4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funcsdom.html#K8" title="FUNCSDOM:func.8">RealFuncZero</a> <font color="Olive" title="b3">A</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> 1</span>)</span> &amp; <font color="Olive" title="b5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funcsdom.html#K9" title="FUNCSDOM:func.9">RealFuncUnit</a> <font color="Olive" title="b3">A</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> holds <br/> for <font color="Olive" title="b6">h</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b3">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>)  ex <font color="Olive" title="b7">a</font>, <font color="Olive" title="b8">b</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <font color="Olive" title="b6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="funcsdom.html#K5" title="FUNCSDOM:func.5">RealFuncAdd</a> <font color="Olive" title="b3">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funcsdom.html#K7" title="FUNCSDOM:func.7">RealFuncExtMult</a> <font color="Olive" title="b3">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b7">a</font>,<font color="Olive" title="b4">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funcsdom.html#K7" title="FUNCSDOM:func.7">RealFuncExtMult</a> <font color="Olive" title="b3">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b8">b</font>,<font color="Olive" title="b5">g</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>)</div></div>
