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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:91_1"/>
( ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) implies ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_1.html#NM1">Function</a> st <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><a NAME="E1:91_1_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:91_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="partfun1.html#E1:91_1_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E3:91_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font> is   <a href="funct_1.html#NM1">Function</a>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T6">GRFUNC_1:6</a></i>;<br/>
<b>hence </b><a NAME="E4:91_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_1.html#NM1">Function</a> st <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div><b>given </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><a NAME="E2:91_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E3:91_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="partfun1.html#E2:91_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><b>hence </b><a NAME="E4:91_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:91"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="partfun1.html#R1" target="_self">tolerates</a> <font color="Maroon">c<sub>2</sub></font> iff ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="ref" href="partfun1.html#T130" target="_self">Th130</a></i>;<br/>


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