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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#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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#M2" title="HIDDEN:mode.2">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#K6" title="FUNCT_4:func.6">--&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#K1" title="FUNCT_7:func.1">+*</a> (<font color="Olive" title="b2">l1</font>,<font color="Olive" title="b4">i1</font>)</span>)</span> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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#M2" title="HIDDEN:mode.2">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#K6" title="FUNCT_4:func.6">--&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#K1" title="FUNCT_7:func.1">+*</a> (<font color="Olive" title="b1">l1</font>,<font color="Olive" title="b3">i1</font>)</span>)</span> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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#M2" title="HIDDEN:mode.2">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#K6" title="FUNCT_4:func.6">--&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#K1" title="FUNCT_7:func.1">+*</a> (<font color="Maroon" title="c3">l1</font>,<font color="Olive" title="b1">i1</font>)</span>)</span> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</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#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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#K6" title="FUNCT_4:func.6">--&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#K1" title="FUNCT_7:func.1">+*</a> (<font color="Maroon" title="c3">l1</font>,<font color="Maroon" title="c5">i1</font>)</span>)</span> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</a> (<font color="Maroon" title="c4">l2</font>,<font color="Maroon" title="c6">i2</font>)</span><br/>







<a NAME="E1:181"/><span class="lab"><font color="Green" title="E82">A1</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" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E2:181"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A2</font></span>: 
<font color="Maroon" title="c3">l1</font> <a href="tarski.html#R2" title="TARSKI: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="E3:181"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</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="#E1:181"><span class="lab"><font color="Green" title="E82">A1</font></span></a>, <a class="ref" href="funct_7.html#T30" target="_self" onmouseover="rs('funct_7/T30')" onmouseout="rh()">Th29</a></span>;<br/>
<a NAME="E4:181"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A3</font></span>: 
<font color="Maroon" title="c4">l2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</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#K6" title="FUNCT_4:func.6">--&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#K17" title="FUNCOP_1:func.17">.--&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#K17" title="FUNCOP_1:func.17">.--&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#K17" title="FUNCOP_1:func.17">.--&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#K17" title="FUNCOP_1:func.17">.--&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" onmouseover="rs('funct_4/T14')" onmouseout="rh()">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</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#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c6">i2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:181"><span class="lab"><font color="Green" title="E83">A2</font></span></a>, <a class="ref" href="funct_7.html#D3" target="_self" onmouseover="rs('funct_7/D3')" onmouseout="rh()">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">X</font> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</a> (<font color="Maroon" title="c3">l1</font>,<font color="Maroon" title="c5">i1</font>)</span>)</span> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</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="#E4:181"><span class="lab"><font color="Green" title="E84">A3</font></span></a>, <a class="ref" href="funct_7.html#D3" target="_self" onmouseover="rs('funct_7/D3')" onmouseout="rh()">Def2</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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