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<span class="kw">let </span><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c1">F</font><br/>  for <font color="Olive" title="b2">W</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c2">G</font><br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font><br/>  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">h</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b6">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b5">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b6">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b4">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b5">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b6">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b6">n</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Olive" title="b5">h</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">V</font> be   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c1">F</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">W</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c2">G</font><br/>  for <font color="Olive" title="b2">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V</font>,<font color="Olive" title="b1">W</font><br/>  for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">h</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">V</font><br/>  for <font color="Olive" title="b5">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b4">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b5">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b3">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b4">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b5">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">n</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Olive" title="b4">h</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">W</font> be   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c2">G</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c4">W</font><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">h</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">V</font><br/>  for <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b3">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b4">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b2">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b3">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b4">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">n</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Olive" title="b3">h</font></span>)</span></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="c3">V</font>,<font color="Maroon" title="c4">W</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">h</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">V</font><br/>  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Olive" title="b2">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Olive" title="b2">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">n</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Olive" title="b2">h</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">h</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">n</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> )</span><br/>















<span class="kw">assume </span><a NAME="E1:46"/><span class="lab"><font color="Green" title="E22">AS</font></span>: 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">n</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span><br/>

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>] <span class="kw">means </span> for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">V</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> $1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> $1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default">$1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>;<br/>
<a NAME="E2:46"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="46_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:46_1"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
 for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">V</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<span class="kw">let </span><font color="Maroon" title="c10">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span><br/>

<span class="lab"><font color="Green" title="E25">A31</font></span>: <font color="Maroon" title="c7">h</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font> = 
<span class="p1">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T13" onmouseover="rs('binom/T13')" onmouseout="rh()">BINOM:13</a></span>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T13" onmouseover="rs('binom/T13')" onmouseout="rh()">BINOM:13</a></span>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T15" onmouseover="rs('binom/T15')" onmouseout="rh()">BINOM:15</a></span>
;<br/>
<span class="lab"><font color="Green" title="E26">A32</font></span>: <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> = 
<span class="p1">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T13" onmouseover="rs('binom/T13')" onmouseout="rh()">BINOM:13</a></span>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T13" onmouseover="rs('binom/T13')" onmouseout="rh()">BINOM:13</a></span>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T15" onmouseover="rs('binom/T15')" onmouseout="rh()">BINOM:15</a></span>
<br/>.= 
2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span>

;<br/>
<span class="lab"><font color="Green" title="E27">A33</font></span>: <font color="Maroon" title="c7">h</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46_1"><span class="lab"><font color="Green" title="E26">A32</font></span></a>, <a class="ref" href="vectsp_1.html#D15" onmouseover="rs('vectsp_1/D15')" onmouseout="rh()">VECTSP_1:def 15</a></span>
;<br/>
<a NAME="E5:46_1"/><span class="lab"><font color="Green" title="E28">A30</font></span>: 
2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="46_1_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:46_1_4"/><span class="lab"><font color="Green" title="E29">A301</font></span>: 
2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> = 
<span class="p1">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T13" onmouseover="rs('binom/T13')" onmouseout="rh()">BINOM:13</a></span>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T13" onmouseover="rs('binom/T13')" onmouseout="rh()">BINOM:13</a></span>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T15" onmouseover="rs('binom/T15')" onmouseout="rh()">BINOM:15</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46_1_4"><span class="lab"><font color="Green" title="E29">A301</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:46_1_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46"><span class="lab"><font color="Green" title="E22">AS</font></span></a>, <a class="ref" href="rlvect_1.html#D10" onmouseover="rs('rlvect_1/D10')" onmouseout="rh()">RLVECT_1:def 10</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="lab"><font color="Green" title="E29">A34</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D14" onmouseover="rs('vectsp_1/D14')" onmouseout="rh()">VECTSP_1:def 14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D16" onmouseover="rs('vectsp_1/D16')" onmouseout="rh()">VECTSP_1:def 16</a>, <a class="txt" href="#E4:46_1"><span class="lab"><font color="Green" title="E27">A33</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:46_1"><span class="lab"><font color="Green" title="E28">A30</font></span></a>, <a class="ref" href="vectsp_1.html#D10" onmouseover="rs('vectsp_1/D10')" onmouseout="rh()">VECTSP_1:def 10</a></span>
<br/>.= 
<font color="Maroon" title="c7">h</font>

;<br/>
<span class="lab"><font color="Green" title="E30">A35</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T15" onmouseover="rs('binom/T15')" onmouseout="rh()">BINOM:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T13" onmouseover="rs('binom/T13')" onmouseout="rh()">BINOM:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T27" onmouseover="rs('rlvect_1/T27')" onmouseout="rh()">RLVECT_1:27</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c7">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T28" onmouseover="rs('rlvect_1/T28')" onmouseout="rh()">RLVECT_1:28</a>, <a class="txt" href="#E6:46_1"><span class="lab"><font color="Green" title="E29">A34</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">V</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T15" onmouseover="rs('rlvect_1/T15')" onmouseout="rh()">RLVECT_1:15</a></span>
<br/>.= 
<font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T4" onmouseover="rs('rlvect_1/T4')" onmouseout="rh()">RLVECT_1:4</a></span>
;<br/>
<span class="lab"><font color="Green" title="E31">A36</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</a></span>
<br/>.= 
<font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</a>, <a class="txt" href="#E6:46_1"><span class="lab"><font color="Green" title="E29">A34</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T13" onmouseover="rs('binom/T13')" onmouseout="rh()">BINOM:13</a></span>
<br/>.= 
<font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T15" onmouseover="rs('binom/T15')" onmouseout="rh()">BINOM:15</a></span>
<br/>.= 
<font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span>

;<br/>
<span class="lab"><font color="Green" title="E32">A3</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46_1"><span class="lab"><font color="Green" title="E24">A2</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T15" onmouseover="rs('binom/T15')" onmouseout="rh()">BINOM:15</a>, <a class="txt" href="#E2:46_1"><span class="lab"><font color="Green" title="E25">A31</font></span></a></span>
;<br/>
<span class="lab"><font color="Green" title="E33">A4</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46_1"><span class="lab"><font color="Green" title="E24">A2</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T13" onmouseover="rs('binom/T13')" onmouseout="rh()">BINOM:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T15" onmouseover="rs('binom/T15')" onmouseout="rh()">BINOM:15</a></span>
;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">r3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">r2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">r1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>;<br/>
<a NAME="E11:46_1"/><span class="lab"><font color="Green" title="E34">A5</font></span>: 
<span class="p1">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> is   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c4">W</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#T3" target="_self" onmouseover="rs('vsdiff_1/T3')" onmouseout="rh()">Th2</a></span>;<br/>
<a NAME="E12:46_1"/><span class="lab"><font color="Green" title="E35">A6</font></span>: 
<span class="p1">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> is   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c4">W</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#T20" target="_self" onmouseover="rs('vsdiff_1/T20')" onmouseout="rh()">Th19</a></span>;<br/>
<a NAME="E13:46_1"/><span class="lab"><font color="Green" title="E36">A7</font></span>: 
<span class="p1">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> is   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c4">W</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#T20" target="_self" onmouseover="rs('vsdiff_1/T20')" onmouseout="rh()">Th19</a></span>;<br/>
<a NAME="E14:46_1"/><span class="lab"><font color="Green" title="E37">A8</font></span>: 
<span class="p1">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> is   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c4">W</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#T3" target="_self" onmouseover="rs('vsdiff_1/T3')" onmouseout="rh()">Th2</a></span>;<br/>
<span class="lab"><font color="Green" title="E38">A9</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="vsdiff_1.html#K7" title="VSDIFF_1:func.7">cD</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#D11" target="_self" onmouseover="rs('vsdiff_1/D11')" onmouseout="rh()">Def8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:46_1"><span class="lab"><font color="Green" title="E35">A6</font></span></a>, <a class="ref" href="vsdiff_1.html#T6" target="_self" onmouseover="rs('vsdiff_1/T6')" onmouseout="rh()">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T29" onmouseover="rs('rlvect_1/T29')" onmouseout="rh()">RLVECT_1:29</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">V</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T15" onmouseover="rs('rlvect_1/T15')" onmouseout="rh()">RLVECT_1:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:46_1"><span class="lab"><font color="Green" title="E30">A35</font></span></a>, <a class="ref" href="rlvect_1.html#T13" onmouseover="rs('rlvect_1/T13')" onmouseout="rh()">RLVECT_1:13</a></span>
;<br/>
<span class="lab"><font color="Green" title="E39">A10</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="vsdiff_1.html#K7" title="VSDIFF_1:func.7">cD</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p5">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#D11" target="_self" onmouseover="rs('vsdiff_1/D11')" onmouseout="rh()">Def8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:46_1"><span class="lab"><font color="Green" title="E35">A6</font></span></a>, <a class="ref" href="vsdiff_1.html#T6" target="_self" onmouseover="rs('vsdiff_1/T6')" onmouseout="rh()">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T28" onmouseover="rs('rlvect_1/T28')" onmouseout="rh()">RLVECT_1:28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binom.html#K5" title="BINOM:func.5">*</a> <span class="p0">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">V</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T15" onmouseover="rs('rlvect_1/T15')" onmouseout="rh()">RLVECT_1:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:46_1"><span class="lab"><font color="Green" title="E31">A36</font></span></a>, <a class="ref" href="rlvect_1.html#T4" onmouseover="rs('rlvect_1/T4')" onmouseout="rh()">RLVECT_1:4</a></span>
;<br/>
<span class="lab"><font color="Green" title="E40">A11</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="vsdiff_1.html#K7" title="VSDIFF_1:func.7">cD</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#D11" target="_self" onmouseover="rs('vsdiff_1/D11')" onmouseout="rh()">Def8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:46_1"><span class="lab"><font color="Green" title="E36">A7</font></span></a>, <a class="txt" href="#E16:46_1"><span class="lab"><font color="Green" title="E39">A10</font></span></a>, <a class="txt" href="#E15:46_1"><span class="lab"><font color="Green" title="E38">A9</font></span></a>, <a class="ref" href="vsdiff_1.html#T6" target="_self" onmouseover="rs('vsdiff_1/T6')" onmouseout="rh()">Th5</a></span>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">x</font>

<br/>.= 
<span class="p1">(<span class="default"><a href="vsdiff_1.html#K5" title="VSDIFF_1:func.5">fD</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#D8" target="_self" onmouseover="rs('vsdiff_1/D8')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:46_1"><span class="lab"><font color="Green" title="E34">A5</font></span></a>, <a class="ref" href="vsdiff_1.html#T4" target="_self" onmouseover="rs('vsdiff_1/T4')" onmouseout="rh()">Th3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#K5" title="VSDIFF_1:func.5">fD</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#D8" target="_self" onmouseover="rs('vsdiff_1/D8')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#K5" title="VSDIFF_1:func.5">fD</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#K5" title="VSDIFF_1:func.5">fD</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#D8" target="_self" onmouseover="rs('vsdiff_1/D8')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#K5" title="VSDIFF_1:func.5">fD</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:46_1"><span class="lab"><font color="Green" title="E37">A8</font></span></a>, <a class="ref" href="vsdiff_1.html#T4" target="_self" onmouseover="rs('vsdiff_1/T4')" onmouseout="rh()">Th3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:46_1"><span class="lab"><font color="Green" title="E37">A8</font></span></a>, <a class="ref" href="vsdiff_1.html#T4" target="_self" onmouseover="rs('vsdiff_1/T4')" onmouseout="rh()">Th3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c9">k</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46_1"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="txt" href="#E9:46_1"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="txt" href="#E10:46_1"><span class="lab"><font color="Green" title="E33">A4</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E19:46_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:46_1"><span class="lab"><font color="Green" title="E40">A11</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:46"/><span class="lab"><font color="Green" title="E24">A12</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ]
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="46_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span></span><br/>

<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">x</font> = 
<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K10" title="FUNCT_2:func.10">/.</a> <font color="Maroon" title="c9">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#D8" target="_self" onmouseover="rs('vsdiff_1/D8')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vsdiff_1.html#D11" target="_self" onmouseover="rs('vsdiff_1/D11')" onmouseout="rh()">Def8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">V</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T4" onmouseover="rs('rlvect_1/T4')" onmouseout="rh()">RLVECT_1:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binom.html#T12" onmouseover="rs('binom/T12')" onmouseout="rh()">BINOM:12</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:46_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E4:46"/>
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S2" onmouseover="rs('nat_1/S2')" onmouseout="rh()">NAT_1:sch 2</a>(<a class="txt" href="#E3:46"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="txt" href="#E2:46"><span class="lab"><font color="Green" title="E23">A1</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E5:46"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vsdiff_1.html#NK9" title="VSDIFF_1:NK.9">fdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c6">x</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="vsdiff_1.html#NK14" title="VSDIFF_1:NK.14">cdif</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">h</font>)</span>)</span> <a href="seqfunc.html#K1" title="SEQFUNC:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">n</font> <a href="binom.html#K5" title="BINOM:func.5">*</a> <font color="Maroon" title="c7">h</font></span>)</span></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
