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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</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">A</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">V</font> being   <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b3">f</font> being   <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Olive" title="b2">V</font>,the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b4">t</font> being  <a href="msaterm.html#NM3" title="MSATERM:NM.3">c-Term</a> of <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">V</font><br/> for <font color="Olive" title="b5">vt</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>  st <font color="Olive" title="b5">vt</font> <a href="msaterm.html#R1" title="MSATERM:pred.1">is_an_evaluation_of</a> <font color="Olive" title="b4">t</font>,<font color="Olive" title="b3">f</font> holds <br/><font color="Olive" title="b4">t</font> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">vt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</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">V</font> being   <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b2">f</font> being   <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Olive" title="b1">V</font>,the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b3">t</font> being  <a href="msaterm.html#NM3" title="MSATERM:NM.3">c-Term</a> of <font color="Maroon" title="c2">A</font>,<font color="Olive" title="b1">V</font><br/> for <font color="Olive" title="b4">vt</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>  st <font color="Olive" title="b4">vt</font> <a href="msaterm.html#R1" title="MSATERM:pred.1">is_an_evaluation_of</a> <font color="Olive" title="b3">t</font>,<font color="Olive" title="b2">f</font> holds <br/><font color="Olive" title="b3">t</font> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">vt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><b>let </b><font color="Maroon" title="c3">V</font> be    <a href="msaterm.html#M4" title="MSATERM:mode.4">Variables</a> of <font color="Maroon" title="c2">A</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="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c3">V</font>,the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b2">t</font> being  <a href="msaterm.html#NM3" title="MSATERM:NM.3">c-Term</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">V</font><br/> for <font color="Olive" title="b3">vt</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>  st <font color="Olive" title="b3">vt</font> <a href="msaterm.html#R1" title="MSATERM:pred.1">is_an_evaluation_of</a> <font color="Olive" title="b2">t</font>,<font color="Olive" title="b1">f</font> holds <br/><font color="Olive" title="b2">t</font> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">vt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><b>let </b><font color="Maroon" title="c4">f</font> be    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c3">V</font>,the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</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="msaterm.html#NM3" title="MSATERM:NM.3">c-Term</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">V</font><br/> for <font color="Olive" title="b2">vt</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>  st <font color="Olive" title="b2">vt</font> <a href="msaterm.html#R1" title="MSATERM:pred.1">is_an_evaluation_of</a> <font color="Olive" title="b1">t</font>,<font color="Maroon" title="c4">f</font> holds <br/><font color="Olive" title="b1">t</font> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">vt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><b>let </b><font color="Maroon" title="c5">t</font> be   <a href="msaterm.html#NM3" title="MSATERM:NM.3">c-Term</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">V</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">vt</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>  st <font color="Olive" title="b1">vt</font> <a href="msaterm.html#R1" title="MSATERM:pred.1">is_an_evaluation_of</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">f</font> holds <br/><font color="Maroon" title="c5">t</font> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">vt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><b>let </b><font color="Maroon" title="c6">vt</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">vt</font> <a href="msaterm.html#R1" title="MSATERM:pred.1">is_an_evaluation_of</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">f</font> implies <font color="Maroon" title="c5">t</font> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">vt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>











<b>assume </b><a NAME="E1:67"/><i><font color="Green" title="E44">A1</font></i>: 
<font color="Maroon" title="c6">vt</font> <a href="msaterm.html#R1" title="MSATERM:pred.1">is_an_evaluation_of</a> <font color="Maroon" title="c5">t</font>,<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"> <font color="Maroon" title="c5">t</font> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">vt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<b>consider </b><font color="Maroon" title="c7">e</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a><b> such that </b><br/><a NAME="E3:67"/><i><font color="Green" title="E45">A2</font></i>: 
( <font color="Maroon" title="c7">e</font> <a href="msaterm.html#R1" title="MSATERM:pred.1">is_an_evaluation_of</a> <font color="Maroon" title="c5">t</font>,<font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c5">t</font> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="ref" href="msaterm.html#D10" target="_self" title="MSATERM:def.10">Def10</a></i>;<br/>
<b>thus </b><a NAME="E4:67"/>
<font color="Maroon" title="c5">t</font> <a href="msaterm.html#K9" title="MSATERM:func.9">@</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">vt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="#E1:67"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="#E3:67"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="msaterm.html#T37" target="_self" title="MSATERM:th.37">Th37</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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