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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">g1</font>, <font color="Maroon" title="c4">g2</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">f1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">g1</font> &amp; <font color="Maroon" title="c2">f2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">g2</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">g2</font> implies <font color="Maroon" title="c1">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">f2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">g1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">g2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:134"/><span class="lab"><font color="Green" title="E59">Z1</font></span>: 
<font color="Maroon" title="c1">f1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">g1</font>
 <span class="kw">and </span><br/><a NAME="E2:134"/><span class="lab"><font color="Green" title="E60">Z2</font></span>: 
<font color="Maroon" title="c2">f2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">g2</font>
 <span class="kw">and </span><br/><a NAME="E3:134"/><span class="lab"><font color="Green" title="E61">Z3</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">f1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">g2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">f2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">g1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">g2</font></span><br/>

<a NAME="E4:134"/><span class="lab"><font color="Green" title="E62">A</font></span>: 
<font color="Maroon" title="c1">f1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">g1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">g2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:134"><span class="lab"><font color="Green" title="E59">Z1</font></span></a>, <a class="txt" href="#E3:134"><span class="lab"><font color="Green" title="E61">Z3</font></span></a>, <a class="ref" href="funct_4.html#T117" target="_self" title="FUNCT_4:th.117">Th125</a></span>;<br/>
<a NAME="E5:134"/>
<font color="Maroon" title="c4">g2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">g1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">g2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" target="_self" title="FUNCT_4:th.25">Th26</a></span>;<br/>
<a NAME="E6:134"/><span class="kw">then </span>
<font color="Maroon" title="c2">f2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">g1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">g2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:134"><span class="lab"><font color="Green" title="E60">Z2</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:134"/>
<font color="Maroon" title="c1">f1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c2">f2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">g1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">g2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:134"><span class="lab"><font color="Green" title="E62">A</font></span></a>, <a class="ref" href="funct_4.html#T87" target="_self" title="FUNCT_4:th.87">Th92</a></span>; <a class="txt" 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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