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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th8</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: PRVECT_2:8</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="prvect_2.html#NM3" title="PRVECT_2:NM.3">RealNormSpace-Sequence</a><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font>, <font color="Olive" title="b4">z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K15" title="PRVECT_1:func.15">carr</a> <font color="Olive" title="b1">G</font></span>)</span><br/>  for <font color="Olive" title="b5">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">x</font> &amp; <font color="Olive" title="b4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prvect_1.html#K12" title="PRVECT_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><a href="prvect_1.html#K18" title="PRVECT_1:func.18">addop</a> <font color="Olive" title="b1">G</font></span>)</span></span><a href="prvect_1.html#K12" title="PRVECT_1:func.12">:]</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>) holds <br/><span class="p1">(<span class="default"><a href="prvect_2.html#K8" title="PRVECT_2:func.8">normsequence</a> (<font color="Olive" title="b1">G</font>,<font color="Olive" title="b4">z</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prvect_2.html#K8" title="PRVECT_2:func.8">normsequence</a> (<font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">x</font>)</span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><a href="prvect_2.html#K8" title="PRVECT_2:func.8">normsequence</a> (<font color="Olive" title="b1">G</font>,<font color="Olive" title="b3">y</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font></div></div>
