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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="aofa_i00.html#V2" title="AOFA_I00:attr.2">Euclidean</a> <a href="aofa_000.html#NM1" title="AOFA_000:NM.1">preIfWhileAlgebra</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">X</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">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="Olive" title="b1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> </span>)</span><br/> for <font color="Olive" title="b3">f</font> being <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a>  <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of <font color="Maroon" title="c1">A</font>, <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Olive" title="b1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> ,<font color="Olive" title="b2">T</font><br/> for <font color="Olive" title="b4">x</font> being   <a href="aofa_i00.html#M1" title="AOFA_I00:mode.1">Variable</a> of <font color="Olive" title="b3">f</font><br/> for <font color="Olive" title="b5">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="Olive" title="b1">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  holds  <span class="p1">(<span class="default"><a href="aofa_i00.html#K42" title="AOFA_I00:func.42">.</a> <font color="Olive" title="b4">x</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">s</font> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <font color="Olive" title="b4">x</font></span><br/><b>let </b><font color="Maroon" title="c2">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="card_4.html#V1" title="CARD_4:attr.1">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="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> </span>)</span><br/> for <font color="Olive" title="b2">f</font> being <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a>  <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of <font color="Maroon" title="c1">A</font>, <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> ,<font color="Olive" title="b1">T</font><br/> for <font color="Olive" title="b3">x</font> being   <a href="aofa_i00.html#M1" title="AOFA_I00:mode.1">Variable</a> of <font color="Olive" title="b2">f</font><br/> for <font color="Olive" title="b4">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="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  holds  <span class="p1">(<span class="default"><a href="aofa_i00.html#K42" title="AOFA_I00:func.42">.</a> <font color="Olive" title="b3">x</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">s</font> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <font color="Olive" title="b3">x</font></span><br/><b>let </b><font color="Maroon" title="c3">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="c2">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">f</font> being <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a>  <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of <font color="Maroon" title="c1">A</font>, <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> ,<font color="Maroon" title="c3">T</font><br/> for <font color="Olive" title="b2">x</font> being   <a href="aofa_i00.html#M1" title="AOFA_I00:mode.1">Variable</a> of <font color="Olive" title="b1">f</font><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="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  holds  <span class="p1">(<span class="default"><a href="aofa_i00.html#K42" title="AOFA_I00:func.42">.</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <font color="Olive" title="b2">x</font></span><br/><b>let </b><font color="Maroon" title="c4">f</font> be  <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a>  <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of <font color="Maroon" title="c1">A</font>, <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> ,<font color="Maroon" title="c3">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">x</font> being   <a href="aofa_i00.html#M1" title="AOFA_I00:mode.1">Variable</a> of <font color="Maroon" title="c4">f</font><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="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  holds  <span class="p1">(<span class="default"><a href="aofa_i00.html#K42" title="AOFA_I00:func.42">.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <font color="Olive" title="b1">x</font></span><br/><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="aofa_i00.html#M1" title="AOFA_I00:mode.1">Variable</a> of <font color="Maroon" title="c4">f</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="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  holds  <span class="p1">(<span class="default"><a href="aofa_i00.html#K42" title="AOFA_I00:func.42">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <font color="Maroon" title="c5">x</font></span><br/><b>let </b><font color="Maroon" title="c6">s</font> be    <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="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="aofa_i00.html#K42" title="AOFA_I00:func.42">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <font color="Maroon" title="c5">x</font></span><br/>











<b>thus </b><span class="p1">(<span class="default"><a href="aofa_i00.html#K42" title="AOFA_I00:func.42">.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">s</font> = 
<font color="Maroon" title="c6">s</font> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="aofa_i00.html#K41" title="AOFA_I00:func.41">^</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c4">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">s</font></span>)</span>
<b>by </b><i><a class="ref" href="aofa_i00.html#D19" target="_self" title="AOFA_I00:def.19">DEFvarexp</a></i>
<br/>.= 
<font color="Maroon" title="c6">s</font> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <font color="Maroon" title="c5">x</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</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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