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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E4">LMEQR001</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: ZMODUL04:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b2">z1</font>, <font color="Olive" title="b3">z2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b4">i1</font>, <font color="Olive" title="b5">i2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  st <font color="Olive" title="b1">V</font> is  <a href="zmodul01.html#V1" title="ZMODUL01:attr.1">Mult-cancelable</a>  holds <br/>( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b2">z1</font>,<font color="Olive" title="b4">i1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b3">z2</font>,<font color="Olive" title="b5">i2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="zmodul04.html#K1" title="ZMODUL04:func.1">EQRZM</a> <font color="Olive" title="b1">V</font> iff ( <font color="Olive" title="b4">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">i2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b5">i2</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">i1</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b3">z2</font> ) )</div></div>
