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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E41">Th38</font></span>: <a NAME="T38"><span class="comment"><font color="firebrick">:: VECTSP11:38</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b3">V1</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b2">K</font><br/>  for <font color="Olive" title="b4">f</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b3">V1</font>,<font color="Olive" title="b3">V1</font><br/>  for <font color="Olive" title="b5">L</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Olive" title="b2">K</font>  st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 holds <br/> ex <font color="Olive" title="b6">h</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b3">V1</font>,<font color="Olive" title="b3">V1</font> st <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Olive" title="b1">n</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="matrlin2.html#K6" title="MATRLIN2:func.6">*</a> <font color="Olive" title="b6">h</font></span>)</span> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Olive" title="b1">n</font></span>)</span> &amp; (  for <font color="Olive" title="b7">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Olive" title="b7">i</font></span>)</span> <a href="matrlin2.html#K6" title="MATRLIN2:func.6">*</a> <font color="Olive" title="b6">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b6">h</font> <a href="matrlin2.html#K6" title="MATRLIN2:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Olive" title="b7">i</font></span>)</span> ) )</div></div>
