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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: INT_6:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">u</font> being   <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b2">m</font> being   <a href="int_6.html#NM1" title="INT_6:NM.1">CR_Sequence</a><br/>  for <font color="Olive" title="b3">z1</font>, <font color="Olive" title="b4">z2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">z1</font> &amp; <font color="Olive" title="b3">z1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Olive" title="b2">m</font> &amp; (  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="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">m</font> holds <br/><font color="Olive" title="b3">z1</font>,<font color="Olive" title="b1">u</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Olive" title="b2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> ) &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">z2</font> &amp; <font color="Olive" title="b4">z2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Olive" title="b2">m</font> &amp; (  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="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">m</font> holds <br/><font color="Olive" title="b4">z2</font>,<font color="Olive" title="b1">u</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Olive" title="b2">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> ) holds <br/><font color="Olive" title="b3">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">z2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="int_6.html#E36"><span class="lab"><font color="Green" title="E33">Lm9</font></span></a></span>;<br/></div></div>
