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<b>let </b><font color="Maroon" title="c1">X</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="c2">Y</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="algstr_0.html#L2" title="ALGSTR_0:struct.2">addLoopStr</a> ;<br/>



<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font>,   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font>) <b>-&gt; </b>   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font> = the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">Y</font> <a href="funcsdom.html#K4" title="FUNCSDOM:func.4">.:</a> $1,$2;<br/>
<b>consider </b><font color="Maroon" title="c3">ADD</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font><b> such that </b><br/><a NAME="E2:2"/><i><font color="Green" title="E2">A1</font></i>: 
for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font> holds  <font color="Maroon" title="c3">ADD</font> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font>)
 <b>from </b><i><a class="ref" href="binop_1.html#S4" title="BINOP_1:sch.4">BINOP_1:sch 4</a>();<br/></i>
<b>take </b>
<font color="Maroon" title="c3">ADD</font>
;<br/>

<b>thus </b><a NAME="E3:2"/>
for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y</font> holds  <font color="Maroon" title="c3">ADD</font> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">Y</font> <a href="funcsdom.html#K4" title="FUNCSDOM:func.4">.:</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font>
 <b>by </b><i><a class="txt" href="lopban_1.html#E2:2"><i><font color="Green" title="E2">A1</font></i></a></i>;<br/>


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