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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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">V1</font>, <font color="Olive" title="b2">V2</font>, <font color="Olive" title="b3">V3</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="b4">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">V1</font>,<font color="Olive" title="b2">V2</font><br/> for <font color="Olive" title="b5">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">V2</font>,<font color="Olive" title="b3">V3</font><br/> for <font color="Olive" title="b6">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="b7">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="b8">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b3">V3</font>  st <font color="Olive" title="b5">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Olive" title="b5">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b6">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b7">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">f</font></span>)</span>,<font color="Olive" title="b6">b1</font>,<font color="Olive" title="b8">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Olive" title="b4">f</font>,<font color="Olive" title="b6">b1</font>,<font color="Olive" title="b7">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Olive" title="b5">g</font>,<font color="Olive" title="b7">b2</font>,<font color="Olive" title="b8">b3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V1</font>, <font color="Maroon" title="c3">V2</font>, <font color="Maroon" title="c4">V3</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c3">V2</font><br/> for <font color="Olive" title="b2">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V2</font>,<font color="Maroon" title="c4">V3</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="Maroon" title="c2">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="Maroon" title="c3">V2</font><br/> for <font color="Olive" title="b5">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>  st <font color="Olive" title="b2">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Olive" title="b2">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">f</font></span>)</span>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b5">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Olive" title="b2">g</font>,<font color="Olive" title="b4">b2</font>,<font color="Olive" title="b5">b3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V2</font>,<font color="Maroon" title="c4">V3</font><br/> for <font color="Olive" title="b2">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="b3">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="b4">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>  st <font color="Olive" title="b1">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Olive" title="b1">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Olive" title="b2">b1</font>,<font color="Olive" title="b4">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Olive" title="b2">b1</font>,<font color="Olive" title="b3">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Olive" title="b1">g</font>,<font color="Olive" title="b3">b2</font>,<font color="Olive" title="b4">b3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">g</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V2</font>,<font color="Maroon" title="c4">V3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">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">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>  st <font color="Maroon" title="c6">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Maroon" title="c6">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Olive" title="b1">b1</font>,<font color="Olive" title="b3">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Olive" title="b1">b1</font>,<font color="Olive" title="b2">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Olive" title="b2">b2</font>,<font color="Olive" title="b3">b3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">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="Red">::  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">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>  st <font color="Maroon" title="c6">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Maroon" title="c6">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Olive" title="b2">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Olive" title="b1">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Olive" title="b1">b2</font>,<font color="Olive" title="b2">b3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>  st <font color="Maroon" title="c6">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Maroon" title="c6">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Olive" title="b1">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Olive" title="b1">b3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c9">b3</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Maroon" title="c6">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> )</span><br/>

















<span class="kw">assume </span><a NAME="E1:63"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
( <font color="Maroon" title="c6">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Maroon" title="c6">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  not  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:63"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E3:63"/><span class="lab"><font color="Green" title="E50">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span><br/>

<span class="lab"><font color="Green" title="E51">A4</font></span>:  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="matrlin.html#T44" target="_self" title="MATRLIN:th.44">Th44</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></span>
;<br/>
<span class="lab"><font color="Green" title="E52">A5</font></span>:  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">b3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="matrlin.html#T44" target="_self" title="MATRLIN:th.44">Th44</a></span>
<br/>.= 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="matrlin.html#T44" target="_self" title="MATRLIN:th.44">Th44</a></span>
;<br/>
<a NAME="E6:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A6</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <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"><span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:63"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></span>;<br/>
<span class="lab"><font color="Green" title="E54">A7</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:63"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></span>
;<br/>
<a NAME="E8:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A8</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></span>;<br/>
<a NAME="E9:63"/>
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">i</font>, <font color="Maroon" title="c11">j</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="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> implies <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> )</span><br/>



<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">b2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> $1</span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c12">d</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font><span class="kw"> such that </span><br/><a NAME="E2:63_4"/><span class="lab"><font color="Green" title="E56">A9</font></span>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font> &amp; ( for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c12">d</font> holds <br/><font color="Maroon" title="c12">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) ) )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="finseq_2.html#S1" title="FINSEQ_2:sch.1">FINSEQ_2:sch 1</a>();<br/></span>
<span class="kw">assume </span><a NAME="E3:63_4"/><span class="lab"><font color="Green" title="E57">A10</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span><br/>

<a NAME="E4:63_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A11</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D5" title="MATRIX_1:def.5">MATRIX_1:def 5</a></span>;<br/>
<a NAME="E5:63_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A12</font></span>: 
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</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="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<span class="lab"><font color="Green" title="E60">A13</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>,<font color="Maroon" title="c11">j</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">d</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_4"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></span>
;<br/>
<a NAME="E7:63_4"/><span class="lab"><font color="Green" title="E61">A14</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c12">d</font> <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> <font color="Maroon" title="c8">b2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_4"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E8:63_4"/><span class="lab"><font color="Green" title="E62">A15</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:63"><span class="lab"><font color="Green" title="E55">A8</font></span></a>, <a class="txt" href="#E6:63"><span class="lab"><font color="Green" title="E53">A6</font></span></a>, <a class="txt" href="#E4:63_4"><span class="lab"><font color="Green" title="E58">A11</font></span></a>, <a class="ref" href="matrix_1.html#D5" title="MATRIX_1:def.5">MATRIX_1:def 5</a></span>;<br/>
<a NAME="E9:63_4"/><span class="lab"><font color="Green" title="E63">A16</font></span>: 
<font color="Maroon" title="c10">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:63_4"><span class="lab"><font color="Green" title="E58">A11</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/>
<a NAME="E10:63_4"/><span class="lab"><font color="Green" title="E64">X</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63_4"><span class="lab"><font color="Green" title="E59">A12</font></span></a></span>;<br/>
<a NAME="E11:63_4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">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="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></span>;<br/>
<a NAME="E12:63_4"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:63_4"><span class="lab"><font color="Green" title="E64">X</font></span></a>, <a class="ref" href="matrix_1.html#D4" title="MATRIX_1:def.4">MATRIX_1:def 4</a></span>;<br/>
<a NAME="E13:63_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A17</font></span>: 
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c9">b3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63_4"><span class="lab"><font color="Green" title="E59">A12</font></span></a>, <a class="ref" href="matrlin.html#T44" target="_self" title="MATRLIN:th.44">Th44</a></span>;<br/>
<a NAME="E14:63_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A18</font></span>: 
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">b3</font>
 
<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/>
<div><span class="lab"><font color="Green" title="E67">A19</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_4_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c13">k</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="Red">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</font> <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> <font color="Maroon" title="c12">d</font> implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>,<font color="Maroon" title="c11">j</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> )</span><br/><span class="kw">assume </span><a NAME="E1:63_4_2"/><span class="lab"><font color="Green" title="E68">A20</font></span>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</font> <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> <font color="Maroon" title="c12">d</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>,<font color="Maroon" title="c11">j</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span><br/><a NAME="E2:63_4_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A21</font></span>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><a NAME="E3:63_4_2"/><span class="lab"><font color="Green" title="E70">A22</font></span>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_4"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="txt" href="#E1:63_4_2"><span class="lab"><font color="Green" title="E68">A20</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><a NAME="E4:63_4_2"/><span class="lab"><font color="Green" title="E71">A23</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></span>;<br/><a NAME="E5:63_4_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A24</font></span>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_4"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="txt" href="#E1:63_4_2"><span class="lab"><font color="Green" title="E68">A20</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><a NAME="E6:63_4_2"/>
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</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="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="txt" href="#E4:63_4"><span class="lab"><font color="Green" title="E58">A11</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E7:63_4_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">k</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63_4_2"><span class="lab"><font color="Green" title="E72">A24</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E8:63_4_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">k</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D5" title="MATRIX_1:def.5">MATRIX_1:def 5</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">p2</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font><span class="kw"> such that </span><br/><a NAME="E10:63_4_2"/><span class="lab"><font color="Green" title="E73">A25</font></span>: 
<font color="Maroon" title="c14">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <span class="kw">and </span><br/><a NAME="E11:63_4_2"/><span class="lab"><font color="Green" title="E74">A26</font></span>: 
<span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c13">k</font>,<font color="Maroon" title="c11">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">p2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">j</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D6" title="MATRIX_1:def.6">MATRIX_1:def 6</a></span>;<br/><span class="lab"><font color="Green" title="E75">A27</font></span>: <font color="Maroon" title="c14">p2</font> = 
<span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="pre_poly.html#K9" title="PRE_POLY:func.9">/.</a> <font color="Maroon" title="c13">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63_4_2"><span class="lab"><font color="Green" title="E72">A24</font></span></a>, <a class="txt" href="#E10:63_4_2"><span class="lab"><font color="Green" title="E73">A25</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">b2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c9">b3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63_4_2"><span class="lab"><font color="Green" title="E70">A22</font></span></a>, <a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></span>
;<br/><a NAME="E13:63_4_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c14">p2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:63_4"><span class="lab"><font color="Green" title="E65">A17</font></span></a>, <a class="ref" href="matrlin.html#D9" target="_self" title="MATRLIN:def.9">Def9</a></span>;<br/><a NAME="E14:63_4_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A28</font></span>: 
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c14">p2</font>
 <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="E15:63_4_2"/>
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_4"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="txt" href="#E1:63_4_2"><span class="lab"><font color="Green" title="E68">A20</font></span></a>, <a class="txt" href="#E4:63_4_2"><span class="lab"><font color="Green" title="E71">A23</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>,<font color="Maroon" title="c11">j</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> = 
<font color="Maroon" title="c14">p2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:63_4_2"><span class="lab"><font color="Green" title="E74">A26</font></span></a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">b2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:63_4_2"><span class="lab"><font color="Green" title="E75">A27</font></span></a>, <a class="txt" href="#E14:63_4_2"><span class="lab"><font color="Green" title="E76">A28</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c12">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_4"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="txt" href="#E2:63_4_2"><span class="lab"><font color="Green" title="E69">A21</font></span></a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E16:63_4"/>
<font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V1</font>
 
;<br/>
<a NAME="E17:63_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A29</font></span>: 
<font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">f</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">consider </span><font color="Maroon" title="c13">p1</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font><span class="kw"> such that </span><br/><a NAME="E19:63_4"/><span class="lab"><font color="Green" title="E69">A30</font></span>: 
<font color="Maroon" title="c13">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font>
 <span class="kw">and </span><br/><a NAME="E20:63_4"/><span class="lab"><font color="Green" title="E70">A31</font></span>: 
<span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">p1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63_4"><span class="lab"><font color="Green" title="E57">A10</font></span></a>, <a class="ref" href="matrix_1.html#D6" title="MATRIX_1:def.6">MATRIX_1:def 6</a></span>;<br/>
<a NAME="E21:63_4"/><span class="lab"><font color="Green" title="E71">A32</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c8">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D9" target="_self" title="MATRLIN:def.9">Def9</a></span>;<br/>
<a NAME="E22:63_4"/><span class="lab"><font color="Green" title="E72">A33</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></span>;<br/>
<a NAME="E23:63_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A34</font></span>: 
<font color="Maroon" title="c10">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c7">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:63_4"><span class="lab"><font color="Green" title="E63">A16</font></span></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></span>;<br/>
<span class="lab"><font color="Green" title="E74">A35</font></span>: <font color="Maroon" title="c13">p1</font> = 
<span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="pre_poly.html#K9" title="PRE_POLY:func.9">/.</a> <font color="Maroon" title="c10">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:63_4"><span class="lab"><font color="Green" title="E63">A16</font></span></a>, <a class="txt" href="#E19:63_4"><span class="lab"><font color="Green" title="E69">A30</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c9">b3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:63_4"><span class="lab"><font color="Green" title="E73">A34</font></span></a>, <a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></span>
;<br/>
<a NAME="E25:63_4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></span>;<br/>
<a NAME="E26:63_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A36</font></span>: 
<font color="Maroon" title="c10">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:63_4"><span class="lab"><font color="Green" title="E63">A16</font></span></a>, <a class="txt" href="#E22:63_4"><span class="lab"><font color="Green" title="E72">A33</font></span></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E76">A37</font></span>:  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span>,<font color="Maroon" title="c10">i</font> = 
<span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_2.html#T18" title="MATRIX_2:th.18">MATRIX_2:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="pre_poly.html#K9" title="PRE_POLY:func.9">/.</a> <font color="Maroon" title="c10">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:63_4"><span class="lab"><font color="Green" title="E75">A36</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c8">b2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:63_4"><span class="lab"><font color="Green" title="E73">A34</font></span></a>, <a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></span>
;<br/>
<a NAME="E28:63_4"/><span class="lab"><font color="Green" title="E77">A38</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> <font color="Maroon" title="c8">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">b2</font>
 
<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="E29:63_4"/>
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:63_4"><span class="lab"><font color="Green" title="E65">A17</font></span></a>, <a class="ref" href="matrlin.html#D9" target="_self" title="MATRLIN:def.9">Def9</a></span>;<br/>
<a NAME="E30:63_4"/><span class="kw">then </span>
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c13">p1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:63_4"><span class="lab"><font color="Green" title="E74">A35</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:63_4"><span class="lab"><font color="Green" title="E70">A31</font></span></a>, <a class="txt" href="#E24:63_4"><span class="lab"><font color="Green" title="E74">A35</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:63_4"><span class="lab"><font color="Green" title="E68">A29</font></span></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p4">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c8">b2</font></span>)</span>,<font color="Maroon" title="c8">b2</font></span>)</span></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#T40" target="_self" title="MATRLIN:th.40">Th40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p3">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c8">b2</font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c8">b2</font></span>)</span></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E21:63_4"><span class="lab"><font color="Green" title="E71">A32</font></span></a>, <a class="ref" href="matrlin.html#T22" target="_self" title="MATRLIN:th.22">Th22</a></span>
<br/>.= 
 <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Maroon" title="c8">b2</font></span>)</span>,<font color="Maroon" title="c12">d</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E14:63_4"><span class="lab"><font color="Green" title="E66">A18</font></span></a>, <a class="txt" href="#E2:63_4"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="txt" href="#E7:63_4"><span class="lab"><font color="Green" title="E61">A14</font></span></a>, <a class="txt" href="#E28:63_4"><span class="lab"><font color="Green" title="E77">A38</font></span></a>, <a class="txt" href="#E21:63_4"><span class="lab"><font color="Green" title="E71">A32</font></span></a>, <a class="ref" href="matrlin.html#T42" target="_self" title="MATRLIN:th.42">Th42</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="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span>,<font color="Maroon" title="c10">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>,<font color="Maroon" title="c11">j</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:63_4"><span class="lab"><font color="Green" title="E76">A37</font></span></a>, <a class="txt" href="#E6:63_4"><span class="lab"><font color="Green" title="E60">A13</font></span></a>, <a class="txt" href="#E15:63_4"><span class="lab"><font color="Green" title="E67">A19</font></span></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:63"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E8:63_4"><span class="lab"><font color="Green" title="E62">A15</font></span></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E10:63"/>
 <a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K10" title="MATRLIN:func.10">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:63"><span class="lab"><font color="Green" title="E54">A7</font></span></a>, <a class="txt" href="#E6:63"><span class="lab"><font color="Green" title="E53">A6</font></span></a>, <a class="ref" href="matrix_1.html#T21" title="MATRIX_1:th.21">MATRIX_1:21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
