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<span class="kw">let </span><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font>, <font color="Maroon" title="c3">Y1</font>, <font color="Maroon" title="c4">Y2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Maroon" title="c3">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">Y2</font> implies  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">Y2</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:137"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
( <font color="Maroon" title="c1">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">X2</font> &amp; <font color="Maroon" title="c3">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">Y2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">Y2</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">f</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">Y1</font> or <font color="Maroon" title="c5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">Y2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:137"/>
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">Y1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">Y2</font></span><br/>

<a NAME="E3:137"/><span class="kw">then </span>
<font color="Maroon" title="c5">f</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c3">Y1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#T120" target="_self" title="PARTFUN1:th.120">Th120</a></span>;<br/>
<a NAME="E4:137"/><span class="kw">then </span>
<font color="Maroon" title="c5">f</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">Y2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:137"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="relset_1.html#T17" title="RELSET_1:th.17">RELSET_1:17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:137"/>
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c4">Y2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#T119" target="_self" title="PARTFUN1:th.119">Th119</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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