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<b>consider </b><font color="Maroon" title="c2">ADD</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E2:4_1_1"/><i><font color="Green" title="E4">A1</font></i>: 
( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font> holds  <font color="Maroon" title="c2">ADD</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> <font color="Olive" title="b1">a</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Olive" title="b2">b</font> ) &amp; <font color="Maroon" title="c2">ADD</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; <font color="Maroon" title="c2">ADD</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> )
 <b>by </b><i><a class="txt" href="real_ns1.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<b>thus </b><a NAME="E3:4_1_1"/>
(  <a href="real_ns1.html#K1" title="REAL_NS1:func.1">Euclid_add</a> <font color="Maroon" title="c1">n</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp;  <a href="real_ns1.html#K1" title="REAL_NS1:func.1">Euclid_add</a> <font color="Maroon" title="c1">n</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> )
 <b>by </b><i><a class="txt" href="real_ns1.html#E2:4_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="real_ns1.html#D1" target="_self" title="REAL_NS1:def.1">Def1</a></i>;<br/>


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