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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>  <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">T</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> </span>)</span><br/> for <font color="Olive" title="b2">c</font> being  <a href="aofa_i00.html#NM2" title="AOFA_I00:NM.2">Enumeration</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b3">f</font> being   <a href="aofa_i00.html#M6" title="AOFA_I00:mode.6">INT-Exec</a> of <font color="Olive" title="b2">c</font>,<font color="Olive" title="b1">T</font><br/> for <font color="Olive" title="b4">t</font> being  <a href="aofa_i00.html#NM5" title="AOFA_I00:NM.5">INT-Expression</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b4">t</font> is    <a href="aofa_i00.html#M3" title="AOFA_I00:mode.3">INT-Expression</a> of  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> ,<font color="Olive" title="b3">f</font></span><br/><b>let </b><font color="Maroon" title="c2">T</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> </span>)</span>; <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">c</font> being  <a href="aofa_i00.html#NM2" title="AOFA_I00:NM.2">Enumeration</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">f</font> being   <a href="aofa_i00.html#M6" title="AOFA_I00:mode.6">INT-Exec</a> of <font color="Olive" title="b1">c</font>,<font color="Maroon" title="c2">T</font><br/> for <font color="Olive" title="b3">t</font> being  <a href="aofa_i00.html#NM5" title="AOFA_I00:NM.5">INT-Expression</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b3">t</font> is    <a href="aofa_i00.html#M3" title="AOFA_I00:mode.3">INT-Expression</a> of  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> ,<font color="Olive" title="b2">f</font></span><br/><b>let </b><font color="Maroon" title="c3">c</font> be   <a href="aofa_i00.html#NM2" title="AOFA_I00:NM.2">Enumeration</a> of <font color="Maroon" title="c1">X</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">f</font> being   <a href="aofa_i00.html#M6" title="AOFA_I00:mode.6">INT-Exec</a> of <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">T</font><br/> for <font color="Olive" title="b2">t</font> being  <a href="aofa_i00.html#NM5" title="AOFA_I00:NM.5">INT-Expression</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b2">t</font> is    <a href="aofa_i00.html#M3" title="AOFA_I00:mode.3">INT-Expression</a> of  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> ,<font color="Olive" title="b1">f</font></span><br/>





<a NAME="E1:51"/><i><font color="Green" title="E35">A0</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="ref" href="aofa_i00.html#T6" target="_self" title="AOFA_I00:th.6">ThNum1</a>, <a class="ref" href="aofa_i00.html#T11" target="_self" title="AOFA_I00:th.11">ThNum5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">c'</font> = <font color="Maroon" title="c3">c</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>, <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="funct_2.html#T4" title="FUNCT_2:th.4">FUNCT_2:4</a></i>;<br/>
<b>set </b><font color="Maroon" title="c5">S</font> =  <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ;<br/>
<b>set </b><font color="Maroon" title="c6">G</font> =  <a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> ;<br/>
<b>set </b><font color="Maroon" title="c7">A</font> =  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> ;<br/>
<b>let </b><font color="Maroon" title="c8">f</font> be    <a href="aofa_i00.html#M6" title="AOFA_I00:mode.6">INT-Exec</a> of <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">T</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">t</font> being  <a href="aofa_i00.html#NM5" title="AOFA_I00:NM.5">INT-Expression</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b1">t</font> is    <a href="aofa_i00.html#M3" title="AOFA_I00:mode.3">INT-Expression</a> of  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> ,<font color="Maroon" title="c8">f</font></span><br/>

<b>consider </b><font color="Maroon" title="c9">v</font> being   <a href="aofa_i00.html#NM4" title="AOFA_I00:NM.4">INT-Variable</a> of <font color="Maroon" title="c1">X</font>;<br/>
<b>let </b><font color="Maroon" title="c10">t</font> be   <a href="aofa_i00.html#NM5" title="AOFA_I00:NM.5">INT-Expression</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">t</font> is    <a href="aofa_i00.html#M3" title="AOFA_I00:mode.3">INT-Expression</a> of  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> ,<font color="Maroon" title="c8">f</font></span><br/>

<a NAME="E4:51"/><i><font color="Green" title="E36">AA</font></i>: 
 <a href="aofa_000.html#K18" title="AOFA_000:func.18">ElementaryInstructions</a> <span class="p1">(<span class="default"><a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="freealg.html#K12" title="FREEALG:func.12">FreeGenSetNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> 
 
<b>by </b><i><a class="ref" href="aofa_000.html#T70" title="AOFA_000:th.70">AOFA_000:70</a></i>;<br/>
<a NAME="E5:51"/><i><font color="Green" title="E37">BB</font></i>: 
 <a href="dtconstr.html#K6" title="DTCONSTR:func.6">Terminals</a> <span class="p1">(<span class="default"><a href="freealg.html#K3" title="FREEALG:func.3">DTConUA</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> 
 
<b>by </b><i><a class="ref" href="freealg.html#T3" title="FREEALG:th.3">FREEALG:3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">v'</font> = <font color="Maroon" title="c9">v</font> as    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> </span>)</span>,<font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">t'</font> = <font color="Maroon" title="c10">t</font> as    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> </span>)</span>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  <b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">cv</font> = <font color="Maroon" title="c4">c'</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">v</font> as    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> </span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>;<br/>
<b>set </b><font color="Maroon" title="c14">v1</font> = <font color="Maroon" title="c13">cv</font> <a href="aofa_i00.html#K18" title="AOFA_I00:func.18">**</a> <font color="Maroon" title="c4">c'</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>
<b>set </b><font color="Maroon" title="c15">t1</font> = <font color="Maroon" title="c12">t'</font> <a href="aofa_i00.html#K18" title="AOFA_I00:func.18">**</a> <font color="Maroon" title="c4">c'</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>
<a NAME="E9:51"/><i><font color="Green" title="E38">CC</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">cv</font> <a href="aofa_i00.html#K18" title="AOFA_I00:func.18">**</a> <font color="Maroon" title="c4">c'</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t'</font> <a href="aofa_i00.html#K18" title="AOFA_I00:func.18">**</a> <font color="Maroon" title="c4">c'</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E10:51"/><b>then </b>
 <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">cv</font> <a href="aofa_i00.html#K18" title="AOFA_I00:func.18">**</a> <font color="Maroon" title="c4">c'</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t'</font> <a href="aofa_i00.html#K18" title="AOFA_I00:func.18">**</a> <font color="Maroon" title="c4">c'</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aofa_000.html#K18" title="AOFA_000:func.18">ElementaryInstructions</a> <span class="p1">(<span class="default"><a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="#E4:51"><i><font color="Green" title="E36">AA</font></i></a>, <a class="txt" href="#E5:51"><i><font color="Green" title="E37">BB</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c16">I</font> =  <a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">cv</font> <a href="aofa_i00.html#K18" title="AOFA_I00:func.18">**</a> <font color="Maroon" title="c4">c'</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">t'</font> <a href="aofa_i00.html#K18" title="AOFA_I00:func.18">**</a> <font color="Maroon" title="c4">c'</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> </span>)</span> ;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="aofa_i00.html#D17" target="_self" title="AOFA_I00:def.17">AOFA_I00:def 17</a> <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">v</font> being  <a href="aofa_i00.html#NM4" title="AOFA_I00:NM.4">INT-Variable</a> of <font color="Maroon" title="c1">X</font> st <font color="Olive" title="b1">v</font>,<font color="Maroon" title="c10">t</font> <a href="aofa_i00.html#R2" title="AOFA_I00:pred.2">form_assignment_wrt</a> <font color="Maroon" title="c8">f</font></span>
<div class="add"><b>take </b><font color="Maroon" title="c17">I</font> = <font color="Maroon" title="c16">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c17">I</font> <a href="aofa_i00.html#R1" title="AOFA_I00:pred.1">is_assignment_wrt</a>  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> ,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c8">f</font></span><br/><b>thus </b><a NAME="E1:51_1"/>
<font color="Maroon" title="c17">I</font> <a href="aofa_i00.html#R1" title="AOFA_I00:pred.1">is_assignment_wrt</a>  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> ,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c8">f</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:51_1_1"/>
<font color="Maroon" title="c17">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aofa_000.html#K18" title="AOFA_000:func.18">ElementaryInstructions</a> <span class="p1">(<span class="default"><a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> </span>)</span>
 <b>by </b><i><a class="txt" href="#E4:51"><i><font color="Green" title="E36">AA</font></i></a>, <a class="txt" href="#E5:51"><i><font color="Green" title="E37">BB</font></i></a>, <a class="txt" href="#E9:51"><i><font color="Green" title="E38">CC</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="aofa_i00.html#D14" target="_self" title="AOFA_I00:def.14">AOFA_I00:def 14</a> <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">v</font> being  <a href="aofa_i00.html#NM4" title="AOFA_I00:NM.4">INT-Variable</a> of <font color="Maroon" title="c1">X</font> ex <font color="Olive" title="b2">t</font> being  <a href="aofa_i00.html#NM5" title="AOFA_I00:NM.5">INT-Expression</a> of <font color="Maroon" title="c1">X</font> st <br/>for <font color="Olive" title="b3">s</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  holds  <font color="Maroon" title="c8">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b3">s</font>,<font color="Maroon" title="c17">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">s</font></span>)</span></span><br/>

<b>take </b>
<font color="Maroon" title="c9">v</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">t</font> being  <a href="aofa_i00.html#NM5" title="AOFA_I00:NM.5">INT-Expression</a> of <font color="Maroon" title="c1">X</font> st <br/>for <font color="Olive" title="b2">s</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  holds  <font color="Maroon" title="c8">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b2">s</font>,<font color="Maroon" title="c17">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">s</font></span>)</span></span><br/>

<b>take </b>
<font color="Maroon" title="c10">t</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">s</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  holds  <font color="Maroon" title="c8">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c17">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font></span>)</span></span><br/>

<a NAME="E2:51_1_1"/>
for <font color="Olive" title="b1">s</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  holds  <font color="Maroon" title="c8">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">s</font>,<span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c11">v'</font></span>)</span> <a href="aofa_i00.html#K17" title="AOFA_I00:func.17">**</a> <font color="Maroon" title="c3">c</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c12">t'</font> <a href="aofa_i00.html#K17" title="AOFA_I00:func.17">**</a> <font color="Maroon" title="c3">c</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">v'</font> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <font color="Olive" title="b1">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">t'</font> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <font color="Olive" title="b1">s</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:51"><i><font color="Green" title="E35">A0</font></i></a>, <a class="ref" href="aofa_i00.html#D28" target="_self" title="AOFA_I00:def.28">INTiwaEXECc</a></i>;<br/>
<b>hence </b><a NAME="E3:51_1_1"/>
for <font color="Olive" title="b1">s</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  holds  <font color="Maroon" title="c8">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c17">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div></div>
<b>end;</b></div>

<b>take </b>
<font color="Maroon" title="c9">v</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">v</font>,<font color="Maroon" title="c10">t</font> <a href="aofa_i00.html#R2" title="AOFA_I00:pred.2">form_assignment_wrt</a> <font color="Maroon" title="c8">f</font></span><br/>

<b>thus </b><a NAME="E13:51"/>
<font color="Maroon" title="c9">v</font>,<font color="Maroon" title="c10">t</font> <a href="aofa_i00.html#R2" title="AOFA_I00:pred.2">form_assignment_wrt</a> <font color="Maroon" title="c8">f</font>
 <b>by </b><i><a class="ref" href="aofa_i00.html#T19" target="_self" title="AOFA_I00:th.19">cII1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
