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<span class="kw">let </span><font color="Maroon" title="c1">a</font> be   <a href="prvect_1.html#NM1" title="PRVECT_1:NM.1">Domain-Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">b</font> being   <a href="prvect_1.html#M1" title="PRVECT_1:mode.1">BinOps</a> of <font color="Maroon" title="c1">a</font>  st ( for <font color="Olive" title="b2">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">a</font> holds  <font color="Olive" title="b1">b</font> <a href="prvect_1.html#K10" title="PRVECT_1:func.10">.</a> <font color="Olive" title="b2">i</font> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>  ) holds <br/><span class="p1"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Olive" title="b1">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">b</font> be    <a href="prvect_1.html#M1" title="PRVECT_1:mode.1">BinOps</a> of <font color="Maroon" title="c1">a</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">a</font> holds  <font color="Maroon" title="c2">b</font> <a href="prvect_1.html#K10" title="PRVECT_1:func.10">.</a> <font color="Olive" title="b1">i</font> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>  ) implies <span class="p1"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:53"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">a</font> holds  <font color="Maroon" title="c2">b</font> <a href="prvect_1.html#K10" title="PRVECT_1:func.10">.</a> <font color="Olive" title="b1">i</font> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c5">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c1">a</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="binop_1.html#D14" title="BINOP_1:def.14">BINOP_1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span>)</span>,<font color="Maroon" title="c5">z</font></span><br/>

<div><span class="lab"><font color="Green" title="E30">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="53_1"><span class="kw">now </span></a><div class="add"><span class="kw">set </span><font color="Maroon" title="c6">xy</font> = <span class="p1"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>;<br/><span class="kw">set </span><font color="Maroon" title="c7">yz</font> = <span class="p1"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>;<br/><span class="kw">let </span><font color="Maroon" title="c8">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">a</font> implies <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span>)</span>,<font color="Maroon" title="c5">z</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">v</font> )</span><br/><span class="kw">assume </span><a NAME="E1:53_1"/>
<font color="Maroon" title="c8">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span>)</span>,<font color="Maroon" title="c5">z</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">v</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">i</font> = <font color="Maroon" title="c8">v</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">a</font> ;<br/><a NAME="E3:53_1"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
( <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font></span>)</span> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="prvect_1.html#K10" title="PRVECT_1:func.10">.</a> <font color="Maroon" title="c9">i</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">z</font> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font></span>)</span></span>)</span> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="prvect_1.html#K10" title="PRVECT_1:func.10">.</a> <font color="Maroon" title="c9">i</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font></span>)</span> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prvect_1.html#D10" target="_self" title="PRVECT_1:def.10">Def10</a></span>;<br/><a NAME="E4:53_1"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
<span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span>)</span>,<font color="Maroon" title="c5">z</font></span>)</span> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="prvect_1.html#K10" title="PRVECT_1:func.10">.</a> <font color="Maroon" title="c9">i</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span>)</span> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">z</font> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prvect_1.html#D10" target="_self" title="PRVECT_1:def.10">Def10</a></span>;<br/><a NAME="E5:53_1"/>
( <font color="Maroon" title="c2">b</font> <a href="prvect_1.html#K10" title="PRVECT_1:func.10">.</a> <font color="Maroon" title="c9">i</font> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a>  &amp; <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span>)</span> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="prvect_1.html#K10" title="PRVECT_1:func.10">.</a> <font color="Maroon" title="c9">i</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="prvect_1.html#K9" title="PRVECT_1:func.9">.</a> <font color="Maroon" title="c9">i</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="prvect_1.html#D10" target="_self" title="PRVECT_1:def.10">Def10</a></span>;<br/><span class="kw">hence </span><a NAME="E6:53_1"/>
<span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span>)</span>,<font color="Maroon" title="c5">z</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:53_1"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E4:53_1"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="ref" href="binop_1.html#D3" title="BINOP_1:def.3">BINOP_1:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E3:53"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">a</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="prvect_1.html#K13" title="PRVECT_1:func.13">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span>)</span>,<font color="Maroon" title="c5">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:53"/>
<span class="p1"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">x</font>,<span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" title="PRVECT_1:func.14">[:</a><span class="default"><font color="Maroon" title="c2">b</font></span><a href="prvect_1.html#K14" title="PRVECT_1:func.14">:]</a></span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span>)</span>,<font color="Maroon" title="c5">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:53"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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