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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E67">ThMBF1</font></span>: <a NAME="T96"><span class="comment"><font color="firebrick">:: ZMODLAT1:96</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V1</font>, <font color="Olive" title="b2">V2</font> being   <a href="vectsp_7.html#V3" title="VECTSP_7:attr.3">free</a>   <a href="zmodul03.html#V1" title="ZMODUL03:attr.1">finite-rank</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b3">b1</font> being    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b1">V1</font><br/>  for <font color="Olive" title="b4">b2</font>, <font color="Olive" title="b5">b3</font> being    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b2">V2</font><br/>  for <font color="Olive" title="b6">f</font> being   <a href="zmodlat1.html#NM5" title="ZMODLAT1:NM.5">bilinear-FrForm</a> of <font color="Olive" title="b1">V1</font>,<font color="Olive" title="b2">V2</font>  st  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="zmodul03.html#K1" title="ZMODUL03:func.1">rank</a> <font color="Olive" title="b1">V1</font> holds <br/> <a href="zmodlat1.html#K18" title="ZMODLAT1:func.18">BilinearM</a> (<font color="Olive" title="b6">f</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b5">b3</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zmodlat1.html#K18" title="ZMODLAT1:func.18">BilinearM</a> (<font color="Olive" title="b6">f</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">b2</font>)</span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zmodlat1.html#K19" title="ZMODLAT1:func.19">inttorealM</a> <span class="p3">(<span class="default"><a href="zmatrlin.html#K10" title="ZMATRLIN:func.10">AutMt</a> (<span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b2">V2</font></span>)</span>,<font color="Olive" title="b5">b3</font>,<font color="Olive" title="b4">b2</font>)</span>)</span></span>)</span> <a href="matrix_0.html#K4" title="MATRIX_0:func.4">@</a></span>)</span></div></div>
