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<a NAME="E1:12"/>
for <font color="Olive" title="b1">r</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a>  holds  <a href="mesfunc7.html#K3" title="MESFUNC7:func.3">multextreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a> ,<font color="Olive" title="b1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">r</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <a href="mesfunc7.html#K3" title="MESFUNC7:func.3">multextreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a> ,<font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r</font></span><br/>

<a NAME="E1:12_1"/>
<a href="mesfunc7.html#K3" title="MESFUNC7:func.3">multextreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a> ,<font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a>  <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <font color="Maroon" title="c1">r</font>
 
<b>by </b><i><a class="ref" href="mesfunc7.html#D2" target="_self" title="MESFUNC7:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E2:12_1"/>
<a href="mesfunc7.html#K3" title="MESFUNC7:func.3">multextreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a> ,<font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r</font>
 <b>by </b><i><a class="ref" href="extreal2.html#T4" title="EXTREAL2:th.4">EXTREAL2:4</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>
<a NAME="E2:12"/><b>then </b><i><font color="Green" title="E6">A1</font></i>: 
 <a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a>  <a href="binop_1.html#R1" title="BINOP_1:pred.1">is_a_left_unity_wrt</a>  <a href="mesfunc7.html#K3" title="MESFUNC7:func.3">multextreal</a> 
 
<b>by </b><i><a class="ref" href="binop_1.html#D5" title="BINOP_1:def.5">BINOP_1:def 5</a></i>;<br/>
<a NAME="E3:12"/>
for <font color="Olive" title="b1">r</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a>  holds  <a href="mesfunc7.html#K3" title="MESFUNC7:func.3">multextreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">r</font>,<a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">r</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <a href="mesfunc7.html#K3" title="MESFUNC7:func.3">multextreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c1">r</font>,<a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r</font></span><br/>

<a NAME="E1:12_2"/>
<a href="mesfunc7.html#K3" title="MESFUNC7:func.3">multextreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c1">r</font>,<a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r</font> <a href="extreal1.html#K2" title="EXTREAL1:func.2">*</a> <a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a> 
 
<b>by </b><i><a class="ref" href="mesfunc7.html#D2" target="_self" title="MESFUNC7:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E2:12_2"/>
<a href="mesfunc7.html#K3" title="MESFUNC7:func.3">multextreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c1">r</font>,<a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r</font>
 <b>by </b><i><a class="ref" href="extreal2.html#T4" title="EXTREAL2:th.4">EXTREAL2:4</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>
<a NAME="E4:12"/><b>then </b>
 <a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a>  <a href="binop_1.html#R2" title="BINOP_1:pred.2">is_a_right_unity_wrt</a>  <a href="mesfunc7.html#K3" title="MESFUNC7:func.3">multextreal</a> 
 
<b>by </b><i><a class="ref" href="binop_1.html#D6" title="BINOP_1:def.6">BINOP_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E5:12"/>
 <a href="mesfunc1.html#K9" title="MESFUNC1:func.9">1.</a>  <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a>  <a href="mesfunc7.html#K3" title="MESFUNC7:func.3">multextreal</a> 
 <b>by </b><i><a class="txt" href="mesfunc7.html#E2:12"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="binop_1.html#D7" title="BINOP_1:def.7">BINOP_1:def 7</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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