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<b>let </b><font color="Maroon" title="c1">f1</font>, <font color="Maroon" title="c2">f2</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="c2">f2</font> implies for <font color="Olive" title="b1">g1</font> being   <a href="algspec1.html#M1" title="ALGSPEC1:mode.1">rng-retract</a> of <font color="Maroon" title="c1">f1</font>  ex <font color="Olive" title="b2">g2</font> being   <a href="algspec1.html#M1" title="ALGSPEC1:mode.1">rng-retract</a> of <font color="Maroon" title="c2">f2</font> st <font color="Olive" title="b1">g1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">g2</font> )</span><br/>

<b>assume </b><a NAME="E1:28"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c1">f1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">f2</font>
 ; <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">g1</font> being   <a href="algspec1.html#M1" title="ALGSPEC1:mode.1">rng-retract</a> of <font color="Maroon" title="c1">f1</font>  ex <font color="Olive" title="b2">g2</font> being   <a href="algspec1.html#M1" title="ALGSPEC1:mode.1">rng-retract</a> of <font color="Maroon" title="c2">f2</font> st <font color="Olive" title="b1">g1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">g2</font></span><br/>

<b>let </b><font color="Maroon" title="c3">g1</font> be    <a href="algspec1.html#M1" title="ALGSPEC1:mode.1">rng-retract</a> of <font color="Maroon" title="c1">f1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">g2</font> being   <a href="algspec1.html#M1" title="ALGSPEC1:mode.1">rng-retract</a> of <font color="Maroon" title="c2">f2</font> st <font color="Maroon" title="c3">g1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">g2</font></span><br/>

<b>consider </b><font color="Maroon" title="c4">g</font> being    <a href="algspec1.html#M1" title="ALGSPEC1:mode.1">rng-retract</a> of <font color="Maroon" title="c2">f2</font>;<br/>
<a NAME="E3:28"/>
( <font color="Maroon" title="c1">f1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c2">f2</font> &amp; <font color="Maroon" title="c2">f2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font> )
 
<b>by </b><i><a class="txt" href="#E1:28"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a>, <a class="ref" href="partfun1.html#T131" title="PARTFUN1:th.131">PARTFUN1:131</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">g2</font> = <font color="Maroon" title="c4">g</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">g1</font> as    <a href="algspec1.html#M1" title="ALGSPEC1:mode.1">rng-retract</a> of <font color="Maroon" title="c2">f2</font> <b>by </b><i><a class="ref" href="algspec1.html#T28" target="_self" title="ALGSPEC1:th.28">Th28</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">g2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">g1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">g2</font></span><br/>

<b>thus </b><a NAME="E5:28"/>
<font color="Maroon" title="c3">g1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">g2</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</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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