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<span class="kw">let </span><font color="Maroon" title="c1">V</font>, <font color="Maroon" title="c2">W</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of  <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">u</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b3">w</font>, <font color="Olive" title="b4">t</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">W</font><br/> for <font color="Olive" title="b5">f</font> being  <a href="hermitan.html#NM2" title="HERMITAN:NM.2">sesquilinear-Form</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font> holds  <font color="Olive" title="b5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">u</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b4">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b3">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b4">t</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b2">u</font>,<font color="Olive" title="b3">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b2">u</font>,<font color="Olive" title="b4">t</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">v1</font>, <font color="Maroon" title="c4">w1</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">w</font>, <font color="Olive" title="b2">t</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">W</font><br/> for <font color="Olive" title="b3">f</font> being  <a href="hermitan.html#NM2" title="HERMITAN:NM.2">sesquilinear-Form</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font> holds  <font color="Olive" title="b3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">w1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b2">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Olive" title="b1">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Olive" title="b2">t</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<font color="Olive" title="b1">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<font color="Olive" title="b2">t</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">w</font>, <font color="Maroon" title="c6">w2</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">W</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="hermitan.html#NM2" title="HERMITAN:NM.2">sesquilinear-Form</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font> holds  <font color="Olive" title="b1">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">w1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">w2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c6">w2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<font color="Maroon" title="c6">w2</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">f</font> be   <a href="hermitan.html#NM2" title="HERMITAN:NM.2">sesquilinear-Form</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">w1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">w2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c6">w2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<font color="Maroon" title="c6">w2</font></span>)</span></span>)</span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c8">v3</font> = <font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c5">w</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">v4</font> = <font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c6">w2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">v5</font> = <font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<font color="Maroon" title="c5">w</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">v6</font> = <font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<font color="Maroon" title="c6">w2</font>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">w1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">w2</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">w2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">w2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bilinear.html#T36" title="BILINEAR:th.36">BILINEAR:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c6">w2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">w</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">w2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#T38" target="_self" title="HERMITAN:th.38">Th38</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c6">w2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<font color="Maroon" title="c5">w</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">w1</font>,<font color="Maroon" title="c6">w2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hermitan.html#T38" target="_self" title="HERMITAN:th.38">Th38</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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