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<b>let </b><font color="Maroon" title="c1">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">o</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b2">e1</font>, <font color="Olive" title="b3">e2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b2">e1</font> <a href="binop_1.html#R1" title="BINOP_1:pred.1">is_a_left_unity_wrt</a> <font color="Olive" title="b1">o</font> &amp; <font color="Olive" title="b3">e2</font> <a href="binop_1.html#R2" title="BINOP_1:pred.2">is_a_right_unity_wrt</a> <font color="Olive" title="b1">o</font> holds <br/><font color="Olive" title="b2">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">e2</font></span><br/><b>let </b><font color="Maroon" title="c2">o</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">A</font>; <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">e1</font>, <font color="Olive" title="b2">e2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">e1</font> <a href="binop_1.html#R1" title="BINOP_1:pred.1">is_a_left_unity_wrt</a> <font color="Maroon" title="c2">o</font> &amp; <font color="Olive" title="b2">e2</font> <a href="binop_1.html#R2" title="BINOP_1:pred.2">is_a_right_unity_wrt</a> <font color="Maroon" title="c2">o</font> holds <br/><font color="Olive" title="b1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">e2</font></span><br/><b>let </b><font color="Maroon" title="c3">e1</font>, <font color="Maroon" title="c4">e2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">e1</font> <a href="binop_1.html#R1" title="BINOP_1:pred.1">is_a_left_unity_wrt</a> <font color="Maroon" title="c2">o</font> &amp; <font color="Maroon" title="c4">e2</font> <a href="binop_1.html#R2" title="BINOP_1:pred.2">is_a_right_unity_wrt</a> <font color="Maroon" title="c2">o</font> implies <font color="Maroon" title="c3">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e2</font> )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:20"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c3">e1</font> <a href="binop_1.html#R1" title="BINOP_1:pred.1">is_a_left_unity_wrt</a> <font color="Maroon" title="c2">o</font>
 <b>and </b><br/><a NAME="E2:20"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c4">e2</font> <a href="binop_1.html#R2" title="BINOP_1:pred.2">is_a_right_unity_wrt</a> <font color="Maroon" title="c2">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e2</font></span><br/>

<b>thus </b><font color="Maroon" title="c3">e1</font> = 
<font color="Maroon" title="c2">o</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">e1</font>,<font color="Maroon" title="c4">e2</font>
<b>by </b><i><a class="txt" href="binop_1.html#E2:20"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="binop_1.html#D6" target="_self" title="BINOP_1:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c4">e2</font>
<b>by </b><i><a class="txt" href="binop_1.html#E1:20"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="binop_1.html#D5" target="_self" title="BINOP_1:def.5">Def5</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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