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<b>let </b><font color="Maroon" title="c6">M</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">M</font> is    <a href="functor0.html#M1" title="FUNCTOR0:mode.1">MSUnTrans</a> of <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font> iff <font color="Maroon" title="c6">M</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c3">f</font> )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">M</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c3">f</font> implies <font color="Maroon" title="c6">M</font> is    <a href="functor0.html#M1" title="FUNCTOR0:mode.1">MSUnTrans</a> of <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font> )</span>
<div class="add"><b>assume </b><a NAME="E1:25_1_1_1"/>
<font color="Maroon" title="c6">M</font> is    <a href="functor0.html#M1" title="FUNCTOR0:mode.1">MSUnTrans</a> of <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">M</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c3">f</font></span><br/><a NAME="E2:25_1_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">I2'</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ex <font color="Olive" title="b2">B'</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Olive" title="b1">I2'</font> ex <font color="Olive" title="b3">f'</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">I1</font>,<font color="Olive" title="b1">I2'</font> st <br/>( <font color="Maroon" title="c3">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">f'</font> &amp; <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">B'</font> &amp; <font color="Maroon" title="c6">M</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c4">A</font>,<font color="Olive" title="b2">B'</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Olive" title="b3">f'</font> )
 <b>by </b><i><a class="ref" href="functor0.html#D4" target="_self" title="FUNCTOR0:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E3:25_1_1_1"/>
<font color="Maroon" title="c6">M</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c3">f</font>
 ; <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>

<b>thus </b><a NAME="E2:25_1_1"/>
( <font color="Maroon" title="c6">M</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c3">f</font> implies <font color="Maroon" title="c6">M</font> is    <a href="functor0.html#M1" title="FUNCTOR0:mode.1">MSUnTrans</a> of <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font> )
 <b>by </b><i><a class="ref" href="functor0.html#D4" target="_self" title="FUNCTOR0:def.4">Def4</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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