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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">x1</font>, <font color="Olive" title="b3">x2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">x1</font>,<font color="Olive" title="b3">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c1">F</font> <a href="funcop_1.html#K3" title="FUNCOP_1:func.3">.:</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Olive" title="b2">x1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Olive" title="b3">x2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">x1</font>,<font color="Olive" title="b3">x2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c1">F</font> <a href="funcop_1.html#K3" title="FUNCOP_1:func.3">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Olive" title="b1">x1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Olive" title="b2">x2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">F</font> implies <font color="Maroon" title="c1">F</font> <a href="funcop_1.html#K3" title="FUNCOP_1:func.3">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c3">x1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c4">x2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">x2</font></span>)</span> )</span><br/>





<b>assume </b><a NAME="E1:7"/><i><font color="Green" title="E5">A1</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">F</font> <a href="funcop_1.html#K3" title="FUNCOP_1:func.3">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c3">x1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c4">x2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">x2</font></span>)</span></span><br/>

<b>set </b><font color="Maroon" title="c5">f</font> = <font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c3">x1</font>;<br/>
<b>set </b><font color="Maroon" title="c6">g</font> = <font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c4">x2</font>;<br/>
<b>thus </b><font color="Maroon" title="c1">F</font> <a href="funcop_1.html#K3" title="FUNCOP_1:func.3">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c3">x1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c4">x2</font></span>)</span> = 
<font color="Maroon" title="c1">F</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseqop.html#T7" target="_self" title="FINSEQOP:th.7">Th7</a></i>
<br/>.= 
<font color="Maroon" title="c2">X</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">x2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="funcop_1.html#T23" title="FUNCOP_1:th.23">FUNCOP_1:23</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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