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<b>let </b><font color="Maroon" title="c1">b</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_2.html#K46" title="BINOP_2:func.46">multint</a>  iff for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  holds  <font color="Maroon" title="c1">b</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  holds  <font color="Maroon" title="c1">b</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> ) implies <font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_2.html#K46" title="BINOP_2:func.46">multint</a>  )</span>
<div class="add"><b>assume </b><a NAME="E1:1_1_1_1"/><i><font color="Green" title="E1">A1</font></i>: 
<font color="Maroon" title="c1">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="binop_2.html#K46" title="BINOP_2:func.46">multint</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i1</font>, <font color="Olive" title="b2">i2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  holds  <font color="Maroon" title="c1">b</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">i1</font>,<font color="Olive" title="b2">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i1</font>,<font color="Olive" title="b2">i2</font></span><br/><b>let </b><font color="Maroon" title="c2">i1</font>, <font color="Maroon" title="c3">i2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">b</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">i1</font>,<font color="Maroon" title="c3">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">i1</font>,<font color="Maroon" title="c3">i2</font></span><br/><a NAME="E2:1_1_1_1"/><i><font color="Green" title="E2">A2</font></i>: 
( <font color="Maroon" title="c2">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  &amp; <font color="Maroon" title="c3">i2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  )
 ;<br/><b>thus </b><font color="Maroon" title="c1">b</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">i1</font>,<font color="Maroon" title="c3">i2</font> = 
<font color="Maroon" title="c2">i1</font> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <font color="Maroon" title="c3">i2</font>
<b>by </b><i><a class="txt" href="#E1:1_1_1_1"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="binop_2.html#D22" title="BINOP_2:def.22">BINOP_2:def 22</a></i>
<br/>.= 
<a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">i1</font>,<font color="Maroon" title="c3">i2</font>
<b>by </b><i><a class="txt" href="#E2:1_1_1_1"><i><font color="Green" title="E2">A2</font></i></a>, <a class="ref" href="binop_2.html#D11" title="BINOP_2:def.11">BINOP_2:def 11</a>, <a class="ref" href="numbers.html#T15" title="NUMBERS:th.15">NUMBERS:15</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:1_1_1"/><i><font color="Green" title="E1">A3</font></i>: 
for <font color="Olive" title="b1">i1</font>, <font color="Olive" title="b2">i2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  holds  <font color="Maroon" title="c1">b</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">i1</font>,<font color="Olive" title="b2">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">i1</font>,<font color="Olive" title="b2">i2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_2.html#K46" title="BINOP_2:func.46">multint</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">i1</font>, <font color="Maroon" title="c3">i2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">b</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">i1</font>,<font color="Maroon" title="c3">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K46" title="BINOP_2:func.46">multint</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">i1</font>,<font color="Maroon" title="c3">i2</font></span><br/><a NAME="E1:1_1_1_2"/><i><font color="Green" title="E2">A4</font></i>: 
( <font color="Maroon" title="c2">i1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  &amp; <font color="Maroon" title="c3">i2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  )
 ;<br/><b>thus </b><font color="Maroon" title="c1">b</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">i1</font>,<font color="Maroon" title="c3">i2</font> = 
<a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">i1</font>,<font color="Maroon" title="c3">i2</font>
<b>by </b><i><a class="txt" href="#E2:1_1_1"><i><font color="Green" title="E1">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c2">i1</font> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <font color="Maroon" title="c3">i2</font>
<b>by </b><i><a class="txt" href="#E1:1_1_1_2"><i><font color="Green" title="E2">A4</font></i></a>, <a class="ref" href="binop_2.html#D11" title="BINOP_2:def.11">BINOP_2:def 11</a>, <a class="ref" href="numbers.html#T15" title="NUMBERS:th.15">NUMBERS:15</a></i>
<br/>.= 
<a href="binop_2.html#K46" title="BINOP_2:func.46">multint</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">i1</font>,<font color="Maroon" title="c3">i2</font>
<b>by </b><i><a class="ref" href="binop_2.html#D22" title="BINOP_2:def.22">BINOP_2:def 22</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:1_1_1"/>
<font color="Maroon" title="c1">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="binop_2.html#K46" title="BINOP_2:func.46">multint</a> 
 <b>by </b><i><a class="ref" href="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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