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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</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">f</font>, <font color="Olive" title="b2">g</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>  st <font color="Olive" title="b2">g</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Olive" title="b1">f</font> holds <br/> <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Olive" title="b1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Olive" title="b2">g</font></span><br/><b>let </b><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">g</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c3">f</font> implies  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c3">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c4">g</font> )</span><br/>





<b>assume </b><a NAME="E1:101"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon" title="c4">g</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c3">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c3">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c4">g</font></span><br/>

<b>let </b><font color="Maroon" title="c5">h</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c3">f</font> or <font color="Maroon" title="c5">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c4">g</font> )</span><br/>

<b>assume </b><a NAME="E2:101"/><i><font color="Green" title="E37">A2</font></i>: 
<font color="Maroon" title="c5">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c3">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="c5">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c4">g</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c6">h'</font> = <font color="Maroon" title="c5">h</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> <b>by </b><i><a class="ref" href="partfun1.html#T168" title="PARTFUN1:th.168">PARTFUN1:168</a></i>;<br/>
<a NAME="E4:101"/><i><font color="Green" title="E38">A3</font></i>: 
<font color="Maroon" title="c6">h'</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>
 
<b>by </b><i><a class="txt" href="#E2:101"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="partfun1.html#T169" title="PARTFUN1:th.169">PARTFUN1:169</a></i>;<br/>
<a NAME="E5:101"/>
<font color="Maroon" title="c4">g</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c6">h'</font>
 
<b>by </b><i><a class="txt" href="#E1:101"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="#E2:101"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="partfun1.html#T140" title="PARTFUN1:th.140">PARTFUN1:140</a>, <a class="ref" href="partfun1.html#T171" title="PARTFUN1:th.171">PARTFUN1:171</a></i>;<br/>
<b>hence </b><a NAME="E6:101"/>
<font color="Maroon" title="c5">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c4">g</font>
 <b>by </b><i><a class="txt" href="#E4:101"><i><font color="Green" title="E38">A3</font></i></a>, <a class="ref" href="partfun1.html#D7" title="PARTFUN1:def.7">PARTFUN1:def 7</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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