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<b>let </b><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">E</font>, <font color="Maroon" title="c3">D</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> ;<br/><b>let </b><font color="Maroon" title="c4">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">D</font>;<br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">D</font>;<br/><b>let </b><font color="Maroon" title="c6">h</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c2">E</font>;<br/><b>let </b><font color="Maroon" title="c7">F</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c3">D</font>;<br/><b>let </b><font color="Maroon" title="c8">H</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c2">E</font>;<br/>















<b>assume </b><a NAME="E1:48"/><i><font color="Green" title="E21">A1</font></i>: 
for <font color="Olive" title="b1">d1</font>, <font color="Olive" title="b2">d2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">D</font> holds  <font color="Maroon" title="c6">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">d1</font>,<font color="Olive" title="b2">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">H</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">d1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">d2</font></span>)</span>
 ;<br/>

<a NAME="E2:48"/><i><font color="Green" title="E22">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E3:48"/><i><font color="Green" title="E23">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E4:48"/><i><font color="Green" title="E24">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">g</font> = <font color="Maroon" title="c1">C</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c4">d</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">D</font> <b>by </b><i><a class="ref" href="funcop_1.html#T58" title="FUNCOP_1:th.58">FUNCOP_1:58</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c6">h</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">[;]</a> <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c5">f</font></span>)</span> = 
<font color="Maroon" title="c6">h</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <font color="Maroon" title="c9">g</font>,<font color="Maroon" title="c5">f</font></span>)</span>
<b>by </b><i><a class="txt" href="finseqop.html#E2:48"><i><font color="Green" title="E22">A2</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c8">H</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>
<b>by </b><i><a class="txt" href="finseqop.html#E1:48"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="finseqop.html#T38" target="_self" title="FINSEQOP:th.38">Th38</a></i>
<br/>.= 
<font color="Maroon" title="c8">H</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">[;]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">d</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>
<b>by </b><i><a class="txt" href="finseqop.html#E3:48"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="funcop_1.html#T23" title="FUNCOP_1:th.23">FUNCOP_1:23</a>, <a class="txt" href="finseqop.html#E4:48"><i><font color="Green" title="E24">A4</font></i></a></i>
;<br/>


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