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<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" 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>, <font color="Olive" title="b2">V2</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b3">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b1">V1</font><br/>  for <font color="Olive" title="b4">b2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b2">V2</font><br/>  for <font color="Olive" title="b5">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="b2">V2</font><br/>  for <font color="Olive" title="b6">W1</font>, <font color="Olive" title="b7">W2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b1">V1</font><br/>  for <font color="Olive" title="b8">U1</font>, <font color="Olive" title="b9">U2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b2">V2</font>  st (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b6">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b8">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b7">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b9">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; <font color="Olive" title="b2">V2</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b8">U1</font>,<font color="Olive" title="b9">U2</font> holds <br/> for <font color="Olive" title="b10">fW1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b6">W1</font>,<font color="Olive" title="b8">U1</font><br/>  for <font color="Olive" title="b11">fW2</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b7">W2</font>,<font color="Olive" title="b9">U2</font>  st <font color="Olive" title="b10">fW1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Olive" title="b6">W1</font> &amp; <font color="Olive" title="b11">fW2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Olive" title="b7">W2</font> holds <br/> for <font color="Olive" title="b12">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b6">W1</font><br/>  for <font color="Olive" title="b13">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b7">W2</font><br/>  for <font color="Olive" title="b14">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b8">U1</font><br/>  for <font color="Olive" title="b15">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b9">U2</font>  st <font color="Olive" title="b12">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b13">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b1</font> &amp; <font color="Olive" title="b14">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b15">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b5">f</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b10">fW1</font>,<font color="Olive" title="b12">w1</font>,<font color="Olive" title="b14">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b11">fW2</font>,<font color="Olive" title="b13">w2</font>,<font color="Olive" title="b15">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">V1</font>, <font color="Maroon" title="c3">V2</font> be   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V1</font><br/>  for <font color="Olive" title="b2">b2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c3">V2</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="Maroon" title="c2">V1</font>,<font color="Maroon" title="c3">V2</font><br/>  for <font color="Olive" title="b4">W1</font>, <font color="Olive" title="b5">W2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V1</font><br/>  for <font color="Olive" title="b6">U1</font>, <font color="Olive" title="b7">U2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c3">V2</font>  st (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b4">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b6">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b5">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b7">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; <font color="Maroon" title="c3">V2</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b6">U1</font>,<font color="Olive" title="b7">U2</font> holds <br/> for <font color="Olive" title="b8">fW1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b4">W1</font>,<font color="Olive" title="b6">U1</font><br/>  for <font color="Olive" title="b9">fW2</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b5">W2</font>,<font color="Olive" title="b7">U2</font>  st <font color="Olive" title="b8">fW1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Olive" title="b4">W1</font> &amp; <font color="Olive" title="b9">fW2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Olive" title="b5">W2</font> holds <br/> for <font color="Olive" title="b10">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b4">W1</font><br/>  for <font color="Olive" title="b11">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b5">W2</font><br/>  for <font color="Olive" title="b12">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b6">U1</font><br/>  for <font color="Olive" title="b13">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b7">U2</font>  st <font color="Olive" title="b10">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b11">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b1</font> &amp; <font color="Olive" title="b12">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b13">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b1</font>,<font color="Olive" title="b2">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b8">fW1</font>,<font color="Olive" title="b10">w1</font>,<font color="Olive" title="b12">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b9">fW2</font>,<font color="Olive" title="b11">w2</font>,<font color="Olive" title="b13">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">b1</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c3">V2</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="Maroon" title="c2">V1</font>,<font color="Maroon" title="c3">V2</font><br/>  for <font color="Olive" title="b3">W1</font>, <font color="Olive" title="b4">W2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V1</font><br/>  for <font color="Olive" title="b5">U1</font>, <font color="Olive" title="b6">U2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c3">V2</font>  st (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b5">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b4">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b6">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; <font color="Maroon" title="c3">V2</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b5">U1</font>,<font color="Olive" title="b6">U2</font> holds <br/> for <font color="Olive" title="b7">fW1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b3">W1</font>,<font color="Olive" title="b5">U1</font><br/>  for <font color="Olive" title="b8">fW2</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b4">W2</font>,<font color="Olive" title="b6">U2</font>  st <font color="Olive" title="b7">fW1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Olive" title="b3">W1</font> &amp; <font color="Olive" title="b8">fW2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Olive" title="b4">W2</font> holds <br/> for <font color="Olive" title="b9">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b3">W1</font><br/>  for <font color="Olive" title="b10">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b4">W2</font><br/>  for <font color="Olive" title="b11">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b5">U1</font><br/>  for <font color="Olive" title="b12">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b6">U2</font>  st <font color="Olive" title="b9">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b10">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Olive" title="b11">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b12">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b2">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Olive" title="b1">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b7">fW1</font>,<font color="Olive" title="b9">w1</font>,<font color="Olive" title="b11">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b8">fW2</font>,<font color="Olive" title="b10">w2</font>,<font color="Olive" title="b12">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">b2</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c3">V2</font>; <a class="txt" 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="c2">V1</font>,<font color="Maroon" title="c3">V2</font><br/>  for <font color="Olive" title="b2">W1</font>, <font color="Olive" title="b3">W2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V1</font><br/>  for <font color="Olive" title="b4">U1</font>, <font color="Olive" title="b5">U2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c3">V2</font>  st (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b2">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b4">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b5">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; <font color="Maroon" title="c3">V2</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b4">U1</font>,<font color="Olive" title="b5">U2</font> holds <br/> for <font color="Olive" title="b6">fW1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">W1</font>,<font color="Olive" title="b4">U1</font><br/>  for <font color="Olive" title="b7">fW2</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b3">W2</font>,<font color="Olive" title="b5">U2</font>  st <font color="Olive" title="b6">fW1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Olive" title="b2">W1</font> &amp; <font color="Olive" title="b7">fW2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Olive" title="b3">W2</font> holds <br/> for <font color="Olive" title="b8">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b2">W1</font><br/>  for <font color="Olive" title="b9">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b3">W2</font><br/>  for <font color="Olive" title="b10">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b4">U1</font><br/>  for <font color="Olive" title="b11">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b5">U2</font>  st <font color="Olive" title="b8">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b9">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Olive" title="b10">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b11">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b1">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b6">fW1</font>,<font color="Olive" title="b8">w1</font>,<font color="Olive" title="b10">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b7">fW2</font>,<font color="Olive" title="b9">w2</font>,<font color="Olive" title="b11">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c6">f</font> be   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c3">V2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">W1</font>, <font color="Olive" title="b2">W2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V1</font><br/>  for <font color="Olive" title="b3">U1</font>, <font color="Olive" title="b4">U2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c3">V2</font>  st (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b1">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b3">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b2">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b4">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; <font color="Maroon" title="c3">V2</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b3">U1</font>,<font color="Olive" title="b4">U2</font> holds <br/> for <font color="Olive" title="b5">fW1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b1">W1</font>,<font color="Olive" title="b3">U1</font><br/>  for <font color="Olive" title="b6">fW2</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">W2</font>,<font color="Olive" title="b4">U2</font>  st <font color="Olive" title="b5">fW1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Olive" title="b1">W1</font> &amp; <font color="Olive" title="b6">fW2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Olive" title="b2">W2</font> holds <br/> for <font color="Olive" title="b7">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b1">W1</font><br/>  for <font color="Olive" title="b8">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b2">W2</font><br/>  for <font color="Olive" title="b9">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b3">U1</font><br/>  for <font color="Olive" title="b10">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b4">U2</font>  st <font color="Olive" title="b7">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b8">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Olive" title="b9">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b10">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b5">fW1</font>,<font color="Olive" title="b7">w1</font>,<font color="Olive" title="b9">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b6">fW2</font>,<font color="Olive" title="b8">w2</font>,<font color="Olive" title="b10">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c7">W1</font>, <font color="Maroon" title="c8">W2</font> be    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">U1</font>, <font color="Olive" title="b2">U2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c3">V2</font>  st (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c7">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c8">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b2">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; <font color="Maroon" title="c3">V2</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b1">U1</font>,<font color="Olive" title="b2">U2</font> holds <br/> for <font color="Olive" title="b3">fW1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c7">W1</font>,<font color="Olive" title="b1">U1</font><br/>  for <font color="Olive" title="b4">fW2</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c8">W2</font>,<font color="Olive" title="b2">U2</font>  st <font color="Olive" title="b3">fW1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c7">W1</font> &amp; <font color="Olive" title="b4">fW2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c8">W2</font> holds <br/> for <font color="Olive" title="b5">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c7">W1</font><br/>  for <font color="Olive" title="b6">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c8">W2</font><br/>  for <font color="Olive" title="b7">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b1">U1</font><br/>  for <font color="Olive" title="b8">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b2">U2</font>  st <font color="Olive" title="b5">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b6">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Olive" title="b7">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b8">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b3">fW1</font>,<font color="Olive" title="b5">w1</font>,<font color="Olive" title="b7">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b4">fW2</font>,<font color="Olive" title="b6">w2</font>,<font color="Olive" title="b8">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c9">U1</font>, <font color="Maroon" title="c10">U2</font> be    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c3">V2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c7">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c9">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; (  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c8">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c10">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  ) &amp; <font color="Maroon" title="c3">V2</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Maroon" title="c9">U1</font>,<font color="Maroon" title="c10">U2</font> implies  for <font color="Olive" title="b1">fW1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c7">W1</font>,<font color="Maroon" title="c9">U1</font><br/>  for <font color="Olive" title="b2">fW2</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c8">W2</font>,<font color="Maroon" title="c10">U2</font>  st <font color="Olive" title="b1">fW1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c7">W1</font> &amp; <font color="Olive" title="b2">fW2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c8">W2</font> holds <br/> for <font color="Olive" title="b3">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c7">W1</font><br/>  for <font color="Olive" title="b4">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c8">W2</font><br/>  for <font color="Olive" title="b5">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c9">U1</font><br/>  for <font color="Olive" title="b6">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c10">U2</font>  st <font color="Olive" title="b3">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b4">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Olive" title="b5">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b6">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b1">fW1</font>,<font color="Olive" title="b3">w1</font>,<font color="Olive" title="b5">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b2">fW2</font>,<font color="Olive" title="b4">w2</font>,<font color="Olive" title="b6">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>) )</span><br/>















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:33"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
(  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c7">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c9">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  )
 <span class="kw">and </span><br/><a NAME="E2:33"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
(  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c8">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c10">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  )
 <span class="kw">and </span><br/><a NAME="E3:33"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
<font color="Maroon" title="c3">V2</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Maroon" title="c9">U1</font>,<font color="Maroon" title="c10">U2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">fW1</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c7">W1</font>,<font color="Maroon" title="c9">U1</font><br/>  for <font color="Olive" title="b2">fW2</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c8">W2</font>,<font color="Maroon" title="c10">U2</font>  st <font color="Olive" title="b1">fW1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c7">W1</font> &amp; <font color="Olive" title="b2">fW2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c8">W2</font> holds <br/> for <font color="Olive" title="b3">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c7">W1</font><br/>  for <font color="Olive" title="b4">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c8">W2</font><br/>  for <font color="Olive" title="b5">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c9">U1</font><br/>  for <font color="Olive" title="b6">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c10">U2</font>  st <font color="Olive" title="b3">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b4">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Olive" title="b5">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b6">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b1">fW1</font>,<font color="Olive" title="b3">w1</font>,<font color="Olive" title="b5">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b2">fW2</font>,<font color="Olive" title="b4">w2</font>,<font color="Olive" title="b6">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/>

<a NAME="E4:33"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
<font color="Maroon" title="c9">U1</font> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <font color="Maroon" title="c10">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a> <font color="Maroon" title="c3">V2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="vectsp_5.html#D4" title="VECTSP_5:def.4">VECTSP_5:def 4</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c11">fW1</font> be   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c7">W1</font>,<font color="Maroon" title="c9">U1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">fW2</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c8">W2</font>,<font color="Maroon" title="c10">U2</font>  st <font color="Maroon" title="c11">fW1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c7">W1</font> &amp; <font color="Olive" title="b1">fW2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c8">W2</font> holds <br/> for <font color="Olive" title="b2">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c7">W1</font><br/>  for <font color="Olive" title="b3">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c8">W2</font><br/>  for <font color="Olive" title="b4">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c9">U1</font><br/>  for <font color="Olive" title="b5">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c10">U2</font>  st <font color="Olive" title="b2">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b3">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Olive" title="b4">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b5">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Olive" title="b2">w1</font>,<font color="Olive" title="b4">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Olive" title="b1">fW2</font>,<font color="Olive" title="b3">w2</font>,<font color="Olive" title="b5">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c12">fW2</font> be   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c8">W2</font>,<font color="Maroon" title="c10">U2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c11">fW1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c7">W1</font> &amp; <font color="Maroon" title="c12">fW2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c8">W2</font> implies  for <font color="Olive" title="b1">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c7">W1</font><br/>  for <font color="Olive" title="b2">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c8">W2</font><br/>  for <font color="Olive" title="b3">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c9">U1</font><br/>  for <font color="Olive" title="b4">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c10">U2</font>  st <font color="Olive" title="b1">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Olive" title="b3">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b4">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Olive" title="b1">w1</font>,<font color="Olive" title="b3">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Olive" title="b2">w2</font>,<font color="Olive" title="b4">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E5:33"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<font color="Maroon" title="c11">fW1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c7">W1</font>
 <span class="kw">and </span><br/><a NAME="E6:33"/><span class="lab"><font color="Green" title="E23">A6</font></span>: 
<font color="Maroon" title="c12">fW2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font> <a href="matrlin2.html#K2" title="MATRLIN2:func.2">|</a> <font color="Maroon" title="c8">W2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c7">W1</font><br/>  for <font color="Olive" title="b2">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c8">W2</font><br/>  for <font color="Olive" title="b3">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c9">U1</font><br/>  for <font color="Olive" title="b4">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c10">U2</font>  st <font color="Olive" title="b1">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Olive" title="b3">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b4">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Olive" title="b1">w1</font>,<font color="Olive" title="b3">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Olive" title="b2">w2</font>,<font color="Olive" title="b4">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/>

<span class="kw">let </span><font color="Maroon" title="c13">w1</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c7">W1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">w2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c8">W2</font><br/>  for <font color="Olive" title="b2">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c9">U1</font><br/>  for <font color="Olive" title="b3">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c10">U2</font>  st <font color="Maroon" title="c13">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b1">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Olive" title="b2">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b3">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Olive" title="b2">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Olive" title="b1">w2</font>,<font color="Olive" title="b3">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c14">w2</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c8">W2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">u1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c9">U1</font><br/>  for <font color="Olive" title="b2">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c10">U2</font>  st <font color="Maroon" title="c13">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c14">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Olive" title="b1">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Olive" title="b1">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Olive" title="b2">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c15">u1</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c9">U1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">u2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c10">U2</font>  st <font color="Maroon" title="c13">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c14">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Maroon" title="c15">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b1">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> holds <br/> <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Olive" title="b1">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c16">u2</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c10">U2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c13">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c14">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Maroon" title="c15">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c16">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> implies  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E7:33"/><span class="lab"><font color="Green" title="E24">A7</font></span>: 
<font color="Maroon" title="c13">w1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c14">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b1</font>
 <span class="kw">and </span><br/><a NAME="E8:33"/><span class="lab"><font color="Green" title="E25">A8</font></span>: 
<font color="Maroon" title="c15">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c16">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)</span><br/>

<a NAME="E9:33"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">w2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:33"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="ref" href="finseq_1.html#T22" title="FINSEQ_1:th.22">FINSEQ_1:22</a></span>;<br/>
<a NAME="E10:33"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
<font color="Maroon" title="c9">U1</font> <a href="vectsp_5.html#K1" title="VECTSP_5:func.1">+</a> <font color="Maroon" title="c10">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c3">V2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="vectsp_5.html#D4" title="VECTSP_5:def.4">VECTSP_5:def 4</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">A</font> =  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>);<br/>
<a NAME="E11:33"/><span class="lab"><font color="Green" title="E28">A11</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D8" title="MATRLIN:def.8">MATRLIN:def 8</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">A2</font> =  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>);<br/>
<a NAME="E12:33"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c8">W2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c16">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c10">U2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T21" target="_self" title="MATRLIN2:th.21">Th21</a></span>;<br/>
<a NAME="E13:33"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A13</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="matrix13.html#T1" title="MATRIX13:th.1">MATRIX13:1</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">A1</font> =  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>);<br/>
<a NAME="E14:33"/><span class="lab"><font color="Green" title="E31">A14</font></span>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c7">W1</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c9">U1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T21" target="_self" title="MATRLIN2:th.21">Th21</a></span>;<br/>
<a NAME="E15:33"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A15</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="matrix13.html#T1" title="MATRIX13:th.1">MATRIX13:1</a></span>;<br/>
<a NAME="E16:33"/><span class="lab"><font color="Green" title="E33">A16</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c16">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="txt" href="#E12:33"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="ref" href="matrix13.html#T1" title="MATRIX13:th.1">MATRIX13:1</a></span>;<br/>
<a NAME="E17:33"/><span class="lab"><font color="Green" title="E34">A17</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E14:33"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="ref" href="matrix13.html#T1" title="MATRIX13:th.1">MATRIX13:1</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E35">A18</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><span class="kw">now </span></a><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c20">uu</font> = <font color="Maroon" title="c15">u1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c16">u2</font> as    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c9">U1</font> <a href="vectsp_5.html#K1" title="VECTSP_5:func.1">+</a> <font color="Maroon" title="c10">U2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:33"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="matrlin2.html#T26" target="_self" title="MATRLIN2:th.26">Th26</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c21">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span> implies  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span>)</span> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span></span>)</span> ) &amp; ( <font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span> implies  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>)</span>)</span> ) )</span><br/><a NAME="E2:33_1"/><span class="lab"><font color="Green" title="E36">A19</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c22">fb</font> = <font color="Maroon" title="c6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font></span>)</span>, <font color="Maroon" title="c23">fbi</font> = <font color="Maroon" title="c6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span></span>)</span></span>)</span> as   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c9">U1</font> <a href="vectsp_5.html#K1" title="VECTSP_5:func.1">+</a> <font color="Maroon" title="c10">U2</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:33"><span class="lab"><font color="Green" title="E27">A10</font></span></a></span>;<br/><a NAME="E4:33_1"/><span class="lab"><font color="Green" title="E37">A20</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:33"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>;<br/><a NAME="E5:33_1"/><span class="lab"><font color="Green" title="E38">A21</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c13">w1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:33"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>;<br/><a NAME="E6:33_1"/><span class="lab"><font color="Green" title="E39">A22</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c11">fW1</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 <font color="Maroon" title="c7">W1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><span class="kw">thus </span><a NAME="E7:33_1"/>
( <font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span> implies  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span>)</span> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span></span>)</span> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span> implies  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>)</span>)</span> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:33_1_1"/><span class="lab"><font color="Green" title="E40">A23</font></span>: 
<font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span>)</span> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:33_1_1"/><span class="lab"><font color="Green" title="E41">A24</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E42">A25</font></span>:  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>) = 
<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:33"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="ref" href="matrix_2.html#T8" title="MATRIX_2:th.8">MATRIX_2:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">fW1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c13">w1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c15">u1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:33_1"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="ref" href="matrlin.html#D8" title="MATRLIN:def.8">MATRLIN:def 8</a></span>
;<br/>
<a NAME="E4:33_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:33"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:33"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E11:33"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/>
<a NAME="E5:33_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A26</font></span>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T5" title="FINSEQ_1:th.5">FINSEQ_1:5</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c4">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font> = 
<font color="Maroon" title="c4">b1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33_1"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E4:33_1"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="#E2:33_1_1"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
<br/>.= 
<font color="Maroon" title="c13">w1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:33"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E5:33_1"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></span>
<br/>.= 
<font color="Maroon" title="c13">w1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:33_1"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
;<br/>
<a NAME="E7:33_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A27</font></span>: 
<font color="Maroon" title="c22">fb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">fW1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">w1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:33"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E6:33_1"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/>
<span class="kw">thus </span> <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>) = 
<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:33"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="#E2:33_1_1"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="txt" href="#E5:33_1_1"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="ref" href="matrix_2.html#T8" title="MATRIX_2:th.8">MATRIX_2:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33_1"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="#E2:33_1_1"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="txt" href="#E5:33_1_1"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c5">b2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33_1"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E4:33_1"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="txt" href="#E1:33_1_1"><span class="lab"><font color="Green" title="E40">A23</font></span></a>, <a class="txt" href="#E2:33_1_1"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="txt" href="#E5:33_1_1"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="ref" href="matrlin.html#D8" title="MATRLIN:def.8">MATRLIN:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c22">fb</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c20">uu</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:33"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E8:33"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="matrlin2.html#T25" target="_self" title="MATRLIN2:th.25">Th25</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">fb</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">U1</font> <a href="vectsp_5.html#K1" title="VECTSP_5:func.1">+</a> <font color="Maroon" title="c10">U2</font></span>)</span></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c20">uu</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D4" title="RLVECT_1:def.4">RLVECT_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">fW1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">w1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c15">u1</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</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="c10">U2</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c16">u2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:33"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E7:33_1_1"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="ref" href="matrlin2.html#T24" target="_self" title="MATRLIN2:th.24">Th24</a>, <a class="ref" href="vectsp_4.html#T12" title="VECTSP_4:th.12">VECTSP_4:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span>)</span> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:33"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="txt" href="#E3:33_1_1"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="ref" href="matrlin2.html#T20" target="_self" title="MATRLIN2:th.20">Th20</a></span>
; <a class="txt" 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><a NAME="E8:33_1"/><span class="lab"><font color="Green" title="E40">A28</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">w2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:33"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>;<br/><a NAME="E9:33_1"/><span class="lab"><font color="Green" title="E41">A29</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c12">fW2</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 <font color="Maroon" title="c8">W2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><span class="kw">thus </span><a NAME="E10:33_1"/>
( <font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span> implies  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>)</span>)</span> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:33_1_2"/><span class="lab"><font color="Green" title="E42">A30</font></span>: 
<font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>)</span>)</span></span><br/>

<a NAME="E2:33_1_2"/><span class="lab"><font color="Green" title="E43">A31</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E3:33_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A32</font></span>: 
<font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:33"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:33"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E13:33"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E11:33"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E2:33_1"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="ref" href="finseq_1.html#T60" title="FINSEQ_1:th.60">FINSEQ_1:60</a></span>;<br/>
<font color="Maroon" title="c4">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span></span>)</span> = 
<font color="Maroon" title="c4">b1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:33"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:33"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E13:33"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E11:33"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E2:33_1"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E4:33_1"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E2:33_1_2"><span class="lab"><font color="Green" title="E43">A31</font></span></a>, <a class="ref" href="finseq_1.html#T60" title="FINSEQ_1:th.60">FINSEQ_1:60</a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
<br/>.= 
<font color="Maroon" title="c14">w2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:33"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E15:33"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E8:33_1"><span class="lab"><font color="Green" title="E40">A28</font></span></a>, <a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></span>
<br/>.= 
<font color="Maroon" title="c14">w2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:33_1"><span class="lab"><font color="Green" title="E40">A28</font></span></a>, <a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
;<br/>
<a NAME="E5:33_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A33</font></span>: 
<font color="Maroon" title="c23">fbi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">fW2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">w2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:33"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E9:33_1"><span class="lab"><font color="Green" title="E41">A29</font></span></a>, <a class="ref" href="funct_1.html#T47" title="FUNCT_1:th.47">FUNCT_1:47</a></span>;<br/>
<span class="lab"><font color="Green" title="E46">A34</font></span>:  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>) = 
<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:33"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E2:33_1_2"><span class="lab"><font color="Green" title="E43">A31</font></span></a>, <a class="ref" href="matrix_2.html#T8" title="MATRIX_2:th.8">MATRIX_2:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">fW2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">w2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c16">u2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:33_1"><span class="lab"><font color="Green" title="E40">A28</font></span></a>, <a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="ref" href="matrlin.html#D8" title="MATRLIN:def.8">MATRLIN:def 8</a></span>
;<br/>
<span class="kw">thus </span> <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span></span>)</span>) = 
<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:33"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:33"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E13:33"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E11:33"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E2:33_1"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E2:33_1_2"><span class="lab"><font color="Green" title="E43">A31</font></span></a>, <a class="ref" href="finseq_1.html#T60" title="FINSEQ_1:th.60">FINSEQ_1:60</a>, <a class="ref" href="matrix_2.html#T8" title="MATRIX_2:th.8">MATRIX_2:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:33"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:33"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E13:33"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E11:33"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E2:33_1"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E1:33_1_2"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E2:33_1_2"><span class="lab"><font color="Green" title="E43">A31</font></span></a>, <a class="ref" href="finseq_1.html#T60" title="FINSEQ_1:th.60">FINSEQ_1:60</a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c21">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p5">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c5">b2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:33_1"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="txt" href="#E3:33_1_2"><span class="lab"><font color="Green" title="E44">A32</font></span></a>, <a class="ref" href="matrlin.html#D8" title="MATRLIN:def.8">MATRLIN:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c23">fbi</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c20">uu</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:33"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E8:33"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="matrlin2.html#T25" target="_self" title="MATRLIN2:th.25">Th25</a></span>
<br/>.= 
<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> <span class="p3">(<span class="default"><font color="Maroon" title="c9">U1</font> <a href="vectsp_5.html#K1" title="VECTSP_5:func.1">+</a> <font color="Maroon" title="c10">U2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c23">fbi</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c20">uu</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D4" title="RLVECT_1:def.4">RLVECT_1:def 4</a></span>
<br/>.= 
<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="c9">U1</font></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c15">u1</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">fW2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">w2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c16">u2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:33"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E5:33_1_2"><span class="lab"><font color="Green" title="E45">A33</font></span></a>, <a class="ref" href="matrlin2.html#T24" target="_self" title="MATRLIN2:th.24">Th24</a>, <a class="ref" href="vectsp_4.html#T12" title="VECTSP_4:th.12">VECTSP_4:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span> <a href="prvect_1.html#K4" title="PRVECT_1:func.4">|-&gt;</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span>,<font color="Maroon" title="c21">i</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:33"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="txt" href="#E6:33_1_2"><span class="lab"><font color="Green" title="E46">A34</font></span></a>, <a class="ref" href="matrlin2.html#T20" target="_self" title="MATRLIN2:th.20">Th20</a></span>
; <a class="txt" 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></div><span class="kw">end;</span></div>
<span class="kw">set </span><font color="Maroon" title="c20">A12</font> = <span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>;<br/>
<a NAME="E19:33"/><span class="lab"><font color="Green" title="E36">A35</font></span>: 
(  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span>)</span> &amp;  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K11" title="MATRIXJ1:func.11">Width</a> <span class="p2"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj1.html#T16" title="MATRIXJ1:th.16">MATRIXJ1:16</a>, <a class="ref" href="matrixj1.html#T20" title="MATRIXJ1:th.20">MATRIXJ1:20</a></span>;<br/>
<a NAME="E20:33"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">u1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c16">u2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:33"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="finseq_1.html#T22" title="FINSEQ_1:th.22">FINSEQ_1:22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:33"/>
 <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K13" title="MATRIXJ1:func.13">block_diagonal</a> (<span class="p1"><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c11">fW1</font>,<font color="Maroon" title="c13">w1</font>,<font color="Maroon" title="c15">u1</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<font color="Maroon" title="c12">fW2</font>,<font color="Maroon" title="c14">w2</font>,<font color="Maroon" title="c16">u2</font>)</span>)</span></span><a href="matrixj1.html#K5" title="MATRIXJ1:func.5">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:33"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E15:33"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E13:33"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E17:33"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="txt" href="#E16:33"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="txt" href="#E19:33"><span class="lab"><font color="Green" title="E36">A35</font></span></a>, <a class="txt" href="#E18:33"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="ref" href="matrixj1.html#T23" title="MATRIXJ1:th.23">MATRIXJ1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
