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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">V1</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b3">f</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">V1</font>,<font color="Olive" title="b2">V1</font><br/>  for <font color="Olive" title="b4">L</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Olive" title="b1">K</font> holds  <font color="Olive" title="b3">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b4">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b2">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> is   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b4">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b2">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b4">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b2">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">K</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V1</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c2">K</font><br/>  for <font color="Olive" title="b2">f</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b1">V1</font>,<font color="Olive" title="b1">V1</font><br/>  for <font color="Olive" title="b3">L</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c2">K</font> holds  <font color="Olive" title="b2">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b3">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b1">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> is   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b3">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b1">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b3">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b1">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">V1</font> be   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c2">K</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c3">V1</font><br/>  for <font color="Olive" title="b2">L</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c2">K</font> holds  <font color="Olive" title="b1">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> is   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c3">V1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">L</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c2">K</font> holds  <font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> is   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">L</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c2">K</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> is   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">fid</font> = <font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">IM</font> =  <a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">fidI</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">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="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> as   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp11.html#T32" target="_self" onmouseover="rs('vectsp11/T32')" onmouseout="rh()">Th32</a></span>;<br/>
<a NAME="E2:43"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p2">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="43_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p2">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> or <font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:43_1"/>
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p2">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:43_1"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p2">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:43_1"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p2">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<a NAME="E5:43_1"/><span class="lab"><font color="Green" title="E32">A3</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43_1"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E6:43_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A4</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
;<br/>
<a NAME="E7:43_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">x</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c3">V1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_4.html#T9" onmouseover="rs('vectsp_4/T9')" onmouseout="rh()">VECTSP_4:9</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">v</font> = <font color="Maroon" title="c10">x</font> as   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c3">V1</font> ;<br/>
<a NAME="E9:43_1"/><span class="lab"><font color="Green" title="E34">A5</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p2">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43_1"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="funct_1.html#T47" onmouseover="rs('funct_1/T47')" onmouseout="rh()">FUNCT_1:47</a></span>;<br/>
<a NAME="E10:43_1"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c8">fidI</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E11:43_1"/><span class="kw">then </span>
( <font color="Maroon" title="c8">fidI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">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="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font> &amp; <font color="Maroon" title="c8">fidI</font> <a href="funct_2.html#K10" title="FUNCT_2:func.10">/.</a> <font color="Maroon" title="c11">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">fidI</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">v</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:43_1"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="ref" href="funct_1.html#T47" onmouseover="rs('funct_1/T47')" onmouseout="rh()">FUNCT_1:47</a>, <a class="ref" href="partfun1.html#D6" onmouseover="rs('partfun1/D6')" onmouseout="rh()">PARTFUN1:def 6</a></span>;<br/>
<a NAME="E12:43_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A6</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">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="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">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="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D3" onmouseover="rs('matrlin/D3')" onmouseout="rh()">MATRLIN:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D4" onmouseover="rs('matrlin/D4')" onmouseout="rh()">MATRLIN:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c11">v</font></span>)</span>

;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E36">A7</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">L</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c11">v</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">L</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">L</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c11">v</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D15" onmouseover="rs('vectsp_1/D15')" onmouseout="rh()">VECTSP_1:def 15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c11">v</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T16" onmouseover="rs('vectsp_1/T16')" onmouseout="rh()">VECTSP_1:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">V1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T14" onmouseover="rs('vectsp_1/T14')" onmouseout="rh()">VECTSP_1:14</a></span>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D4" onmouseover="rs('rlvect_1/D4')" onmouseout="rh()">RLVECT_1:def 4</a></span>
;<br/>
<a NAME="E15:43_1"/>
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">L</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c11">v</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:43_1"><span class="lab"><font color="Green" title="E33">A4</font></span></a>, <a class="ref" href="vectsp_4.html#T21" onmouseover="rs('vectsp_4/T21')" onmouseout="rh()">VECTSP_4:21</a></span>;<br/>
<a NAME="E16:43_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">v</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:43_1"><span class="lab"><font color="Green" title="E36">A7</font></span></a>, <a class="txt" href="#E12:43_1"><span class="lab"><font color="Green" title="E35">A6</font></span></a>, <a class="ref" href="vectsp_4.html#T20" onmouseover="rs('vectsp_4/T20')" onmouseout="rh()">VECTSP_4:20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:43_1"/>
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:43_1"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="txt" href="#E9:43_1"><span class="lab"><font color="Green" title="E34">A5</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:43"/>
<font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> is   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K1" title="VECTSP11:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="vectsp11.html#E9"><span class="lab"><font color="Green" title="E9">Lm1</font></span></a>, <a class="ref" href="funct_2.html#T6" onmouseover="rs('funct_2/T6')" onmouseout="rh()">FUNCT_2:6</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
