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<b>let </b><font color="Maroon" title="c1">g</font>, <font color="Maroon" title="c2">h</font>, <font color="Maroon" title="c3">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:57"/><i><font color="Green" title="E32">A1</font></i>: 
<font color="Maroon" title="c1">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">h</font>
 <b>and </b><br/><a NAME="E2:57"/><i><font color="Green" title="E33">A2</font></i>: 
<font color="Maroon" title="c2">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">sproduct</a> <font color="Maroon" title="c3">f</font>
 ;<br/>

<a NAME="E3:57"/><i><font color="Green" title="E34">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">h</font>
 
<b>by </b><i><a class="txt" href="ami_1.html#E1:57"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E4:57"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">h</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f</font>
 
<b>by </b><i><a class="txt" href="ami_1.html#E2:57"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="ami_1.html#T25" target="_self" title="AMI_1:th.25">Th25</a></i>;<br/>
<a NAME="E5:57"/><b>then </b><i><font color="Green" title="E35">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f</font>
 
<b>by </b><i><a class="txt" href="ami_1.html#E3:57"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:57_1"/><i><font color="Green" title="E36">A5</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">g</font>
 ;<br/><a NAME="E2:57_1"/><b>then </b>
<font color="Maroon" title="c2">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="txt" href="ami_1.html#E2:57"><i><font color="Green" title="E33">A2</font></i></a>, <a class="txt" href="ami_1.html#E3:57"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="ami_1.html#T25" target="_self" title="AMI_1:th.25">Th25</a></i>;<br/><b>hence </b><a NAME="E3:57_1"/>
<font color="Maroon" title="c1">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="txt" href="ami_1.html#E1:57"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="ami_1.html#E1:57_1"><i><font color="Green" title="E36">A5</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:57"/>
<font color="Maroon" title="c1">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">sproduct</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="txt" href="ami_1.html#E5:57"><i><font color="Green" title="E35">A4</font></i></a>, <a class="ref" href="ami_1.html#D16" target="_self" title="AMI_1:def.16">Def16</a></i>;<br/>


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