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<b>reconsider </b><font color="Maroon">FAB</font> =  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i><a class="ref" href="funct_2.html#T11">FUNCT_2:11</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b>for <font color="Olive">tv</font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()  st <font color="Olive">tv</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>2</sub></font> holds <br/>for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() holds  <font color="Olive">tv</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Maroon">a<sub>1</sub></font>,<font color="Olive">a</font>);<br/>
<div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="dtconstr.html#K6">Terminals</a> <font color="Maroon">F<sub>1</sub></font>();<br/><b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>3</sub></font>() = <font color="Maroon">F<sub>6</sub></font>(<font color="Maroon">x</font>,<font color="Maroon">a<sub>1</sub></font>);<br/><b>consider </b><font color="Maroon">y</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()<b> such that </b><br/><a NAME="E2:25_1_1"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() holds  <font color="Maroon">y</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">FUNCT_2:sch 4</a>();<br/></i><a NAME="E3:25_1_1"/>
( <font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">y</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>3</sub></font>() )
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>then reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font> <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/><b>take </b><font color="Maroon">y</font> = <font color="Maroon">y</font>;<br/><b>thus </b><a NAME="E5:25_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">x</font>,<font color="Maroon">y</font>]
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">TV</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="dtconstr.html#K6">Terminals</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">FAB</font><b> such that </b><br/><a NAME="E4:25_1"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">e</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="dtconstr.html#K6">Terminals</a> <font color="Maroon">F<sub>1</sub></font>() holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">e</font>,<font color="Maroon">TV</font> <a href="funct_2.html#K3">.</a> <font color="Olive">e</font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S3">FUNCT_2:sch 3</a>();<br/></i>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b>for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()<br/> for <font color="Olive">ntv</font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()  st <font color="Olive">ntv</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>4</sub></font> holds <br/><font color="Olive">ntv</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>7</sub></font>(<font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>,<font color="Maroon">a<sub>3</sub></font>,<font color="Olive">a</font>);<br/>
<div><i><font color="Green">E38</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="dtconstr.html#K7">NonTerminals</a> <font color="Maroon">F<sub>1</sub></font>();<br/><b>let </b><font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font>, <font color="Maroon">z</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font>;<br/><b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>3</sub></font>() = <font color="Maroon">F<sub>7</sub></font>(<font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>,<font color="Maroon">a<sub>1</sub></font>);<br/><b>consider </b><font color="Maroon">fab</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()<b> such that </b><br/><a NAME="E2:25_1_2"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() holds  <font color="Maroon">fab</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">FUNCT_2:sch 4</a>();<br/></i><a NAME="E3:25_1_2"/>
( <font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">fab</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">fab</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>3</sub></font>() )
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>then reconsider </b><font color="Maroon">fab</font> = <font color="Maroon">fab</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font> <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/><b>take </b><font color="Maroon">fab</font> = <font color="Maroon">fab</font>;<br/><b>thus </b><a NAME="E5:25_1_2"/>
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>,<font color="Maroon">fab</font>]
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">NTV</font> being   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="dtconstr.html#K7">NonTerminals</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span>,<font color="Maroon">FAB</font>,<font color="Maroon">FAB</font></span><a href="zfmisc_1.html#K3">:]</a></span>,<font color="Maroon">FAB</font><b> such that </b><br/><a NAME="E7:25_1"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">x</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="dtconstr.html#K7">NonTerminals</a> <font color="Maroon">F<sub>1</sub></font>()<br/> for <font color="Olive">y</font>, <font color="Olive">z</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font> holds  <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Olive">z</font>,<font color="Maroon">NTV</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="bintree1.html#K3" target="_self">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Olive">z</font></span><a href="bintree1.html#K3" target="_self">]</a></span>]
 <b>from </b><i><a class="ref" href="multop_1.html#S1">MULTOP_1:sch 1</a>();<br/></i>
<b>reconsider </b><font color="Maroon">f1'</font> = <font color="Maroon">F<sub>4</sub></font>() as   <a href="funct_2.html#NM1">Function</a> of  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">FAB</font> ;<br/>
<b>reconsider </b><font color="Maroon">f2'</font> = <font color="Maroon">F<sub>5</sub></font>() as   <a href="funct_2.html#NM1">Function</a> of  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">FAB</font> ;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="dtconstr.html#NM2">Terminal</a> of <font color="Maroon">F<sub>1</sub></font>()) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font> = <font color="Maroon">TV</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="dtconstr.html#NM3">NonTerminal</a> of <font color="Maroon">F<sub>1</sub></font>(),   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ,   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font>,   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font> = <font color="Maroon">NTV</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="bintree1.html#K3" target="_self">[</a><span class="default"><font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>4</sub></font>,<font color="Maroon">a<sub>5</sub></font></span><a href="bintree1.html#K3" target="_self">]</a></span>;<br/>
<div><i><font color="Green">E41</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_3"><b>now </b></a><div class="add"><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">t</font> be   <a href="dtconstr.html#NM2">Terminal</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>consider </b><font color="Maroon">g</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()<b> such that </b><br/><a NAME="E2:25_1_3_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K8">root-tree</a> <font color="Maroon">t</font></span>)</span> &amp; ( for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() holds  <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Maroon">t</font>,<font color="Olive">a</font>) ) )
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">TVt</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E4:25_1_3_1"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">TV</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">TVt</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">TVt</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>() &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">TVt</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>3</sub></font>() )
 <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">TVt</font> = <font color="Maroon">TVt</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_3_1_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:25_1_3_1_1"/>
<font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>thus </b><a NAME="E2:25_1_3_1_1"/>
<font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">TVt</font>
 <b>by </b><i/>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E3:25_1_3_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>()
 ;<br/><b>then reconsider </b><font color="Maroon">xx</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() ;<br/><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font> = 
<font color="Maroon">F<sub>6</sub></font>(<font color="Maroon">t</font>,<font color="Maroon">xx</font>)
<b>by </b><i/>
<br/>.= 
<font color="Maroon">TVt</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font>
<b>by </b><i>, </i>
;<br/><b>hence </b><a NAME="E6:25_1_3_1_1"/>
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">TVt</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:25_1_3_1"/>
<font color="Maroon">f1'</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K8">root-tree</a> <font color="Maroon">t</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">t</font>)
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div>
<b>end;</b></div><b>let </b><font color="Maroon">nt</font> be   <a href="dtconstr.html#NM3">NonTerminal</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>let </b><font color="Maroon">tl</font> be    <a href="dtconstr.html#M1">Element</a> of  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">tr</font> be    <a href="dtconstr.html#M1">Element</a> of  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">F<sub>1</sub></font>();<br/><b>let </b><font color="Maroon">rtl</font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">rtr</font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>assume </b><a NAME="E2:25_1_3"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">rtl</font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1" target="_self">root-label</a> <font color="Maroon">tl</font> &amp; <font color="Maroon">rtr</font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1" target="_self">root-label</a> <font color="Maroon">tr</font> &amp; <font color="Maroon">nt</font> <a href="lang1.html#R1">==&gt;</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">rtl</font>,<font color="Maroon">rtr</font></span><a href="lang1.html#K4">*&gt;</a></span> )
 ;<br/><b>let </b><font color="Maroon">xl</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font>, <font color="Maroon">xr</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font>;<br/><b>assume </b><a NAME="E3:25_1_3"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">xl</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">tl</font> &amp; <font color="Maroon">xr</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">tr</font> )
 ;<br/><b>consider </b><font color="Maroon">g</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>(), <font color="Maroon">ff1</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>(), <font color="Maroon">ff2</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()<b> such that </b><br/><a NAME="E5:25_1_3"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">nt</font> <a href="trees_4.html#K10">-tree</a> <font color="Maroon">tl</font>,<font color="Maroon">tr</font></span>)</span> &amp; <font color="Maroon">ff1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() <a href="funct_2.html#K3">.</a> <font color="Maroon">tl</font> &amp; <font color="Maroon">ff2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() <a href="funct_2.html#K3">.</a> <font color="Maroon">tr</font> &amp; ( for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() holds  <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>7</sub></font>(<font color="Maroon">nt</font>,<font color="Maroon">ff1</font>,<font color="Maroon">ff2</font>,<font color="Olive">a</font>) ) )
 <b>by </b><i>, </i>;<br/><b>consider </b><font color="Maroon">ntvnt</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E7:25_1_3"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">ntvnt</font> <a href="hidden.html#R1">=</a> <font color="Maroon">NTV</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="bintree1.html#K3" target="_self">[</a><span class="default"><font color="Maroon">nt</font>,<font color="Maroon">xl</font>,<font color="Maroon">xr</font></span><a href="bintree1.html#K3" target="_self">]</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">ntvnt</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>() &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">ntvnt</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>3</sub></font>() )
 <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">ntvnt</font> = <font color="Maroon">ntvnt</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_3_2"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:25_1_3_2"/>
<font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>thus </b><a NAME="E2:25_1_3_2"/>
<font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">ntvnt</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E3:25_1_3_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>()
 ;<br/><b>then reconsider </b><font color="Maroon">xx</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() ;<br/><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font> = 
<font color="Maroon">F<sub>7</sub></font>(<font color="Maroon">nt</font>,<font color="Maroon">xl</font>,<font color="Maroon">xr</font>,<font color="Maroon">xx</font>)
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">ntvnt</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font>
<b>by </b><i>, </i>
;<br/><b>hence </b><a NAME="E6:25_1_3_2"/>
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">ntvnt</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E10:25_1_3"/>
<font color="Maroon">f1'</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">nt</font> <a href="trees_4.html#K10">-tree</a> <font color="Maroon">tl</font>,<font color="Maroon">tr</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">nt</font>,<font color="Maroon">rtl</font>,<font color="Maroon">rtr</font>,<font color="Maroon">xl</font>,<font color="Maroon">xr</font>)
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E62</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_4"><b>now </b></a><div class="add"><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">t</font> be   <a href="dtconstr.html#NM2">Terminal</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>consider </b><font color="Maroon">g</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()<b> such that </b><br/><a NAME="E2:25_1_4_1"/><i><font color="Green">E63</font></i>: 
( <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>5</sub></font>() <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K8">root-tree</a> <font color="Maroon">t</font></span>)</span> &amp; ( for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() holds  <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>6</sub></font>(<font color="Maroon">t</font>,<font color="Olive">a</font>) ) )
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">TVt</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E4:25_1_4_1"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">TV</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">TVt</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">TVt</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>() &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">TVt</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>3</sub></font>() )
 <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">TVt</font> = <font color="Maroon">TVt</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_4_1_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:25_1_4_1_1"/>
<font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>thus </b><a NAME="E2:25_1_4_1_1"/>
<font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">TVt</font>
 <b>by </b><i/>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E3:25_1_4_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>()
 ;<br/><b>then reconsider </b><font color="Maroon">xx</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() ;<br/><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font> = 
<font color="Maroon">F<sub>6</sub></font>(<font color="Maroon">t</font>,<font color="Maroon">xx</font>)
<b>by </b><i/>
<br/>.= 
<font color="Maroon">TVt</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font>
<b>by </b><i>, </i>
;<br/><b>hence </b><a NAME="E6:25_1_4_1_1"/>
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">TVt</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:25_1_4_1"/>
<font color="Maroon">f2'</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K8">root-tree</a> <font color="Maroon">t</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">t</font>)
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div>
<b>end;</b></div><b>let </b><font color="Maroon">nt</font> be   <a href="dtconstr.html#NM3">NonTerminal</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>let </b><font color="Maroon">tl</font> be    <a href="dtconstr.html#M1">Element</a> of  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">tr</font> be    <a href="dtconstr.html#M1">Element</a> of  <a href="dtconstr.html#K4">TS</a> <font color="Maroon">F<sub>1</sub></font>();<br/><b>let </b><font color="Maroon">rtl</font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">rtr</font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>assume </b><a NAME="E2:25_1_4"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">rtl</font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1" target="_self">root-label</a> <font color="Maroon">tl</font> &amp; <font color="Maroon">rtr</font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1" target="_self">root-label</a> <font color="Maroon">tr</font> &amp; <font color="Maroon">nt</font> <a href="lang1.html#R1">==&gt;</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">rtl</font>,<font color="Maroon">rtr</font></span><a href="lang1.html#K4">*&gt;</a></span> )
 ;<br/><b>let </b><font color="Maroon">xl</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font>, <font color="Maroon">xr</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">FAB</font>;<br/><b>assume </b><a NAME="E3:25_1_4"/><i><font color="Green">E67</font></i>: 
( <font color="Maroon">xl</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">tl</font> &amp; <font color="Maroon">xr</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">tr</font> )
 ;<br/><b>consider </b><font color="Maroon">g</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>(), <font color="Maroon">ff1</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>(), <font color="Maroon">ff2</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()<b> such that </b><br/><a NAME="E5:25_1_4"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>5</sub></font>() <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">nt</font> <a href="trees_4.html#K10">-tree</a> <font color="Maroon">tl</font>,<font color="Maroon">tr</font></span>)</span> &amp; <font color="Maroon">ff1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>5</sub></font>() <a href="funct_2.html#K3">.</a> <font color="Maroon">tl</font> &amp; <font color="Maroon">ff2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>5</sub></font>() <a href="funct_2.html#K3">.</a> <font color="Maroon">tr</font> &amp; ( for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() holds  <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>7</sub></font>(<font color="Maroon">nt</font>,<font color="Maroon">ff1</font>,<font color="Maroon">ff2</font>,<font color="Olive">a</font>) ) )
 <b>by </b><i>, </i>;<br/><b>consider </b><font color="Maroon">ntvnt</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E7:25_1_4"/><i><font color="Green">E69</font></i>: 
( <font color="Maroon">ntvnt</font> <a href="hidden.html#R1">=</a> <font color="Maroon">NTV</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="bintree1.html#K3" target="_self">[</a><span class="default"><font color="Maroon">nt</font>,<font color="Maroon">xl</font>,<font color="Maroon">xr</font></span><a href="bintree1.html#K3" target="_self">]</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">ntvnt</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>() &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">ntvnt</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>3</sub></font>() )
 <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">ntvnt</font> = <font color="Maroon">ntvnt</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_4_2"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:25_1_4_2"/>
<font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>thus </b><a NAME="E2:25_1_4_2"/>
<font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">ntvnt</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E3:25_1_4_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>()
 ;<br/><b>then reconsider </b><font color="Maroon">xx</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() ;<br/><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font> = 
<font color="Maroon">F<sub>7</sub></font>(<font color="Maroon">nt</font>,<font color="Maroon">xl</font>,<font color="Maroon">xr</font>,<font color="Maroon">xx</font>)
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">ntvnt</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">xx</font>
<b>by </b><i>, </i>
;<br/><b>hence </b><a NAME="E6:25_1_4_2"/>
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">ntvnt</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E10:25_1_4"/>
<font color="Maroon">f2'</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">nt</font> <a href="trees_4.html#K10">-tree</a> <font color="Maroon">tl</font>,<font color="Maroon">tr</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">nt</font>,<font color="Maroon">rtl</font>,<font color="Maroon">rtr</font>,<font color="Maroon">xl</font>,<font color="Maroon">xr</font>)
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div>
<a NAME="E12:25_1"/>
<font color="Maroon">f1'</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f2'</font>
 
<b>from </b><i><a class="ref" href="bintree1.html#S4" target="_self">BINTREE1:sch 4</a>(, );<br/></i>
<b>hence </b><a NAME="E13:25_1"/>
<font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>5</sub></font>()
 ;<br/>


</div>
