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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th23</font></span>: <a NAME="T23"><span class="comment"><font color="firebrick">:: NAGATA_1:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b2">ADD</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">T</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>)</span>)</span>  st (  for <font color="Olive" title="b3">f1</font>, <font color="Olive" title="b4">f2</font> being   <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <font color="Olive" title="b1">T</font> holds  <font color="Olive" title="b2">ADD</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">f1</font>,<font color="Olive" title="b4">f2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f1</font> <a href="nagata_1.html#K3" title="NAGATA_1:func.3">+</a> <font color="Olive" title="b4">f2</font> ) holds <br/>( <font color="Olive" title="b2">ADD</font> is  <a href="setwiseo.html#V1" title="SETWISEO:attr.1">having_a_unity</a>  &amp; <font color="Olive" title="b2">ADD</font> is  <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a>  &amp; <font color="Olive" title="b2">ADD</font> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>  )</div></div>
