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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: VECTSP_8:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b4">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">B</font>  st <font color="Olive" title="b4">f</font> is  <a href="vectsp_1.html#V13" title="VECTSP_1:attr.13">additive</a>  &amp; <font color="Olive" title="b4">f</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  holds <br/> <a href="vectsp_8.html#K6" title="VECTSP_8:func.6">FuncLatt</a> <font color="Olive" title="b4">f</font> is   <a href="vectsp_8.html#NM4" title="VECTSP_8:NM.4">sup-Semilattice-Homomorphism</a> of <span class="p1">(<span class="default"><a href="vectsp_8.html#K1" title="VECTSP_8:func.1">lattice</a> <font color="Olive" title="b2">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="vectsp_8.html#K1" title="VECTSP_8:func.1">lattice</a> <font color="Olive" title="b3">B</font></span>)</span></div></div>
