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<b>let </b><font color="Maroon" title="c2">IT</font>, <font color="Maroon" title="c3">IT'</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" title="NORMFORM:func.12">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:36_2_2"/><i><font color="Green" title="E32">A5</font></i>: 
for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" title="NORMFORM:func.12">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> holds  <font color="Maroon" title="c2">IT</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Olive" title="b1">u</font></span>)</span> <a href="heyting1.html#K7" title="HEYTING1:func.7">=&gt;&gt;</a> <span class="p2">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Olive" title="b2">v</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E2:36_2_2"/><i><font color="Green" title="E33">A6</font></i>: 
for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" title="NORMFORM:func.12">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> holds  <font color="Maroon" title="c3">IT'</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Olive" title="b1">u</font></span>)</span> <a href="heyting1.html#K7" title="HEYTING1:func.7">=&gt;&gt;</a> <span class="p2">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Olive" title="b2">v</font></span>)</span></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">v</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" title="NORMFORM:func.12">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span>;<br/><b>thus </b><font color="Maroon" title="c2">IT</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font> = 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c4">u</font></span>)</span> <a href="heyting1.html#K7" title="HEYTING1:func.7">=&gt;&gt;</a> <span class="p2">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c5">v</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="heyting1.html#E1:36_2_2"><i><font color="Green" title="E32">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">IT'</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">v</font>
<b>by </b><i><a class="txt" href="heyting1.html#E2:36_2_2"><i><font color="Green" title="E33">A6</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:36_2_2"/>
<font color="Maroon" title="c2">IT</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">IT'</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</a></i>;<br/>


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