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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be   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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">X</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><br/>  for <font color="Olive" title="b2">l1</font>, <font color="Olive" title="b3">l2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font><br/>  for <font color="Olive" title="b4">i1</font>, <font color="Olive" title="b5">i2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds  <font color="Olive" title="b1">X</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">(<font color="Olive" title="b2">l1</font>,<font color="Olive" title="b3">l2</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Olive" title="b4">i1</font>,<font color="Olive" title="b5">i2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Olive" title="b2">l1</font>,<font color="Olive" title="b4">i1</font>)</span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Olive" title="b3">l2</font>,<font color="Olive" title="b5">i2</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">l1</font>, <font color="Olive" title="b2">l2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font><br/>  for <font color="Olive" title="b3">i1</font>, <font color="Olive" title="b4">i2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds  <font color="Maroon" title="c2">X</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">(<font color="Olive" title="b1">l1</font>,<font color="Olive" title="b2">l2</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Olive" title="b3">i1</font>,<font color="Olive" title="b4">i2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Olive" title="b1">l1</font>,<font color="Olive" title="b3">i1</font>)</span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Olive" title="b2">l2</font>,<font color="Olive" title="b4">i2</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">l1</font>, <font color="Maroon" title="c4">l2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">i1</font>, <font color="Olive" title="b2">i2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds  <font color="Maroon" title="c2">X</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c3">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Olive" title="b1">i1</font>,<font color="Olive" title="b2">i2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">l1</font>,<font color="Olive" title="b1">i1</font>)</span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c4">l2</font>,<font color="Olive" title="b2">i2</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">i1</font>, <font color="Maroon" title="c6">i2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">X</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c3">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">i2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">l1</font>,<font color="Maroon" title="c5">i1</font>)</span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c6">i2</font>)</span><br/>







<a NAME="E1:186"/><span class="lab"><font color="Green" title="E86">A0</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E2:186"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">A1</font></span>: 
<font color="Maroon" title="c3">l1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">X</font>
 
;<br/>
<a NAME="E3:186"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">l1</font>,<font color="Maroon" title="c5">i1</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:186"><span class="lab"><font color="Green" title="E86">A0</font></span></a>, <a class="ref" href="funct_7.html#T30" target="_self" title="FUNCT_7:th.30">Th32</a></span>;<br/>
<a NAME="E4:186"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A2</font></span>: 
<font color="Maroon" title="c4">l2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">l1</font>,<font color="Maroon" title="c5">i1</font>)</span>)</span>
 
;<br/>
<span class="kw">thus </span><font color="Maroon" title="c2">X</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c3">l1</font>,<font color="Maroon" title="c4">l2</font>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">i2</font>)</span>)</span> = 
<font color="Maroon" title="c2">X</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">l1</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c5">i1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">l2</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c6">i2</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">l1</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c5">i1</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l2</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c6">i2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">l1</font>,<font color="Maroon" title="c5">i1</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l2</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c6">i2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:186"><span class="lab"><font color="Green" title="E87">A1</font></span></a>, <a class="ref" href="funct_7.html#D3" target="_self" title="FUNCT_7:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">l1</font>,<font color="Maroon" title="c5">i1</font>)</span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c6">i2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:186"><span class="lab"><font color="Green" title="E88">A2</font></span></a>, <a class="ref" href="funct_7.html#D3" target="_self" title="FUNCT_7:def.3">Def3</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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