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<b>let </b><font color="Maroon">b</font> be   <a href="binop_1.html#NM2">BinOp</a> of  <a href="numbers.html#K4">INT</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:4_1_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">b</font> <a href="funct_2.html#R2">=</a>  <a href="binop_2.html#K44">addint</a> 
 ;<br/><b>let </b><font color="Maroon">i1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">i2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> ;<br/><a NAME="E2:4_1_1_1"/>
( <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K4">INT</a>  &amp; <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K4">INT</a>  )
 ;<br/><a NAME="E3:4_1_1_1"/><b>then </b><i><font color="Green">E47</font></i>: 
( <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  &amp; <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  )
 <b>by </b><i><a class="ref" href="numbers.html#T15">NUMBERS:15</a></i>;<br/><b>thus </b><font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">i1</font>,<font color="Maroon">i2</font> = 
<font color="Maroon">i1</font> <a href="binop_2.html#K20">+</a> <font color="Maroon">i2</font>
<b>by </b><i>, <a class="ref" href="binop_2.html#D20">BINOP_2:def 20</a></i>
<br/>.= 
<a href="binop_2.html#K33">addreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">i1</font>,<font color="Maroon">i2</font>
<b>by </b><i>, <a class="ref" href="binop_2.html#D9">BINOP_2:def 9</a></i>
;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:4_1_1"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">i1</font>, <font color="Olive">i2</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  holds  <font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <font color="Olive">i1</font>,<font color="Olive">i2</font> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K33">addreal</a>  <a href="binop_1.html#K1">.</a> <font color="Olive">i1</font>,<font color="Olive">i2</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">i2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> ;<br/><a NAME="E1:4_1_1_2"/>
( <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K4">INT</a>  &amp; <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K4">INT</a>  )
 ;<br/><a NAME="E2:4_1_1_2"/><b>then </b><i><font color="Green">E51</font></i>: 
( <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  &amp; <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  )
 <b>by </b><i><a class="ref" href="numbers.html#T15">NUMBERS:15</a></i>;<br/><b>thus </b><font color="Maroon">b</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">i1</font>,<font color="Maroon">i2</font> = 
<a href="binop_2.html#K33">addreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">i1</font>,<font color="Maroon">i2</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">i1</font> <a href="binop_2.html#K20">+</a> <font color="Maroon">i2</font>
<b>by </b><i>, <a class="ref" href="binop_2.html#D9">BINOP_2:def 9</a></i>
<br/>.= 
<a href="binop_2.html#K44">addint</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">i1</font>,<font color="Maroon">i2</font>
<b>by </b><i><a class="ref" href="binop_2.html#D20">BINOP_2:def 20</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:4_1_1"/>
<font color="Maroon">b</font> <a href="funct_2.html#R2">=</a>  <a href="binop_2.html#K44">addint</a> 
 <b>by </b><i><a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


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