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<div><span class="lab"><font color="Green" title="E1">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">x</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">li</font>,<font color="Maroon" title="c4">k</font>)</span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">li</font>,<font color="Maroon" title="c4">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E1:1_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">li</font>,<font color="Maroon" title="c4">k</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">li</font>,<font color="Maroon" title="c4">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><a NAME="E2:1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E2">A2</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">s</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T30" title="FUNCT_7:th.30">FUNCT_7:30</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:1_1_1_1_1"/>
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">li</font> or <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">li</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E3">A3</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">li</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">li</font>,<font color="Maroon" title="c4">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">then </span><span class="lab"><font color="Green" title="E4">A4</font></span>:  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> = 
 <a href="memstr_0.html#K2" title="MEMSTR_0:func.2">ObjectKind</a> <font color="Maroon" title="c3">li</font>

<br/>.= 
 <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T11" title="SCMFSA_2:th.11">SCMFSA_2:11</a></span>
;<br/><a NAME="E3:1_1_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">li</font>,<font color="Maroon" title="c4">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1_1_1_1_1_1"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="txt" href="#E2:1_1_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="ref" href="funct_7.html#T31" title="FUNCT_7:th.31">FUNCT_7:31</a></span>;<br/><span class="kw">hence </span><a NAME="E4:1_1_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">li</font>,<font color="Maroon" title="c4">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:1_1_1_1_1_1"><span class="lab"><font color="Green" title="E4">A4</font></span></a>, <a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:1_1_1_1_1_2"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">li</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">li</font>,<font color="Maroon" title="c4">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">li</font>,<font color="Maroon" title="c4">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T32" title="FUNCT_7:th.32">FUNCT_7:32</a></span>;<br/><span class="kw">hence </span><a NAME="E3:1_1_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">li</font>,<font color="Maroon" title="c4">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:1_1_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="ref" href="funct_1.html#D14" title="FUNCT_1:def.14">FUNCT_1:def 14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">thus </span><a NAME="E2:1_1_1"/>
<font color="Maroon" title="c2">s</font> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> (<font color="Maroon" title="c3">li</font>,<font color="Maroon" title="c4">k</font>) is   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></a>, <a class="ref" href="funct_1.html#D14" title="FUNCT_1:def.14">FUNCT_1:def 14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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