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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">n</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"> for <font color="Olive" title="b1">K</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>  st <font color="Maroon" title="c1">i</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> <font color="Maroon" title="c2">n</font> holds <br/> <a href="laplace.html#K2" title="LAPLACE:func.2">Delete</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Olive" title="b1">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Olive" title="b1">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">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"> ( <font color="Maroon" title="c1">i</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> <font color="Maroon" title="c2">n</font> implies  <a href="laplace.html#K2" title="LAPLACE:func.2">Delete</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c3">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> )</span><br/>





<span class="kw">assume </span><a NAME="E1:6"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<font color="Maroon" title="c1">i</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> <font color="Maroon" title="c2">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="laplace.html#K2" title="LAPLACE:func.2">Delete</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c3">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span><br/>

<a NAME="E2:6"/><span class="kw">then </span>
<font color="Maroon" title="c2">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 
;<br/>
<a NAME="E3:6"/><span class="kw">then </span>
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></span>;<br/>
<a NAME="E4:6"/><span class="kw">then </span>
<font color="Maroon" title="c2">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></span>;<br/>
<a NAME="E5:6"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T78" title="FINSEQ_1:th.78">FINSEQ_1:78</a></span>;<br/>
<a NAME="E6:6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A2</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="matrix13.html#K3" title="MATRIX13:func.3">{</a><span class="default"><font color="Maroon" title="c1">i</font></span><a href="matrix13.html#K3" title="MATRIX13:func.3">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="stirl2_1.html#T65" title="STIRL2_1:th.65">STIRL2_1:65</a></span>;<br/>
<span class="kw">thus </span> <a href="laplace.html#K2" title="LAPLACE:func.2">Delete</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c1">i</font> = 
 <a href="matrix_2.html#K9" title="MATRIX_2:func.9">Deleting</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="laplace.html#D1" title="LAPLACE:def.1">LAPLACE:def 1</a></span>
<br/>.= 
 <a href="matrix13.html#K6" title="MATRIX13:func.6">Segm</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="matrix13.html#K3" title="MATRIX13:func.3">{</a><span class="default"><font color="Maroon" title="c1">i</font></span><a href="matrix13.html#K3" title="MATRIX13:func.3">}</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="matrix13.html#K3" title="MATRIX13:func.3">{</a><span class="default"><font color="Maroon" title="c1">i</font></span><a href="matrix13.html#K3" title="MATRIX13:func.3">}</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix13.html#T58" title="MATRIX13:th.58">MATRIX13:58</a></span>
<br/>.= 
 <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c3">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="vectsp11.html#T2" target="_self" title="VECTSP11:th.2">Th2</a>, <a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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