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<span class="kw">let </span><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b2">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b3">D1</font>, <font color="Olive" title="b4">D2</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b5">SQ2</font>, <font color="Olive" title="b6">SQ1</font> being  <font color="Olive">b<sub>2</sub></font> <a href="fomodel4.html#V2" title="FOMODEL4:attr.2">-sequents-like</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Olive" title="b3">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b4">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Olive" title="b5">SQ2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Olive" title="b3">D1</font></span>)</span>,<font color="Maroon" title="c1">m</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">SQ1</font> &amp; <font color="Olive" title="b1">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Olive" title="b4">D2</font></span>)</span>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">SQ2</font> holds <br/><font color="Olive" title="b1">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b4">D2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">SQ1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">Z</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">  for <font color="Olive" title="b1">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b2">D1</font>, <font color="Olive" title="b3">D2</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">SQ2</font>, <font color="Olive" title="b5">SQ1</font> being  <font color="Olive">b<sub>1</sub></font> <a href="fomodel4.html#V2" title="FOMODEL4:attr.2">-sequents-like</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Olive" title="b2">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Olive" title="b4">SQ2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Olive" title="b2">D1</font></span>)</span>,<font color="Maroon" title="c1">m</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">SQ1</font> &amp; <font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Olive" title="b3">D2</font></span>)</span>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">SQ2</font> holds <br/><font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">D2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">SQ1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">S</font> be   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">D1</font>, <font color="Olive" title="b2">D2</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c4">S</font><br/>  for <font color="Olive" title="b3">SQ2</font>, <font color="Olive" title="b4">SQ1</font> being  <font color="Maroon" title="c4">S</font> <a href="fomodel4.html#V2" title="FOMODEL4:attr.2">-sequents-like</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Olive" title="b1">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Olive" title="b3">SQ2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Olive" title="b1">D1</font></span>)</span>,<font color="Maroon" title="c1">m</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">SQ1</font> &amp; <font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Olive" title="b2">D2</font></span>)</span>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">SQ2</font> holds <br/><font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">D2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">SQ1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">D1</font>, <font color="Maroon" title="c6">D2</font> be   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c4">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">SQ2</font>, <font color="Olive" title="b2">SQ1</font> being  <font color="Maroon" title="c4">S</font> <a href="fomodel4.html#V2" title="FOMODEL4:attr.2">-sequents-like</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c5">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Olive" title="b1">SQ2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c5">D1</font></span>)</span>,<font color="Maroon" title="c1">m</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">SQ1</font> &amp; <font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c6">D2</font></span>)</span>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">SQ2</font> holds <br/><font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">SQ1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">SQ2</font>, <font color="Maroon" title="c8">SQ1</font> be  <font color="Maroon" title="c4">S</font> <a href="fomodel4.html#V2" title="FOMODEL4:attr.2">-sequents-like</a>   <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">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Maroon" title="c7">SQ2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c5">D1</font></span>)</span>,<font color="Maroon" title="c1">m</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font> &amp; <font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c6">D2</font></span>)</span>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">SQ2</font> implies <font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font> )</span><br/>















<span class="kw">reconsider </span><font color="Maroon" title="c9">mm</font> = <font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c10">nn</font> = <font color="Maroon" title="c2">n</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">D3</font> = <font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">O1</font> =  <a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c5">D1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">O2</font> =  <a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c6">D2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">O3</font> =  <a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">X</font> = <font color="Maroon" title="c8">SQ1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">Y</font> = <font color="Maroon" title="c7">SQ2</font>;<br/>
<span class="kw">assume </span><a NAME="E2:68"/><span class="lab"><font color="Green" title="E33">B11</font></span>: 
( <font color="Maroon" title="c5">D1</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">SQ2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c5">D1</font></span>)</span>,<font color="Maroon" title="c1">m</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font> or  not <font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c6">D2</font></span>)</span>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">SQ2</font> or <font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:68"/><span class="lab"><font color="Green" title="E34">B0</font></span>: 
( <font color="Maroon" title="c7">SQ2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c5">D1</font></span>)</span>,<font color="Maroon" title="c1">m</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font> &amp; <font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c6">D2</font></span>)</span>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">SQ2</font> )
 ; <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="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font></span><br/>

<a NAME="E4:68"/><span class="lab"><font color="Green" title="E35">B2</font></span>: 
( <font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font> &amp; <font color="Maroon" title="c5">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font> &amp; <font color="Maroon" title="c6">D2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<a NAME="E5:68"/><span class="kw">then </span>
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c5">D1</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E33"><span class="lab"><font color="Green" title="E28">Lm17</font></span></a>, <a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E33">B11</font></span></a></span>;<br/>
<a NAME="E6:68"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">BB3</font></span>: 
<font color="Maroon" title="c7">SQ2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:68"><span class="lab"><font color="Green" title="E34">B0</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E7:68"/><span class="lab"><font color="Green" title="E37">B6</font></span>: 
<font color="Maroon" title="c8">SQ1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">m</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E7"><span class="lab"><font color="Green" title="E6">Lm4</font></span></a></span>;<br/>
<a NAME="E8:68"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c6">D2</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">SQ2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">n</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">SQ2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:68"><span class="lab"><font color="Green" title="E35">B2</font></span></a>, <a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E33">B11</font></span></a>, <a class="txt" href="fomodel4.html#E33"><span class="lab"><font color="Green" title="E28">Lm17</font></span></a></span>;<br/>
<a NAME="E9:68"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">B5</font></span>: 
<font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">n</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">SQ2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:68"><span class="lab"><font color="Green" title="E34">B0</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p3">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span></span>)</span>,<font color="Maroon" title="c10">nn</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p3">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span></span>)</span>,<font color="Maroon" title="c9">mm</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#T77" title="FUNCT_7:th.77">FUNCT_7:77</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c2">n</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p3">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">m</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:68"><span class="lab"><font color="Green" title="E37">B6</font></span></a>, <a class="ref" href="funct_1.html#T13" title="FUNCT_1:th.13">FUNCT_1:13</a></span>
;<br/>
<a NAME="E11:68"/><span class="kw">then </span>
<span class="p1">(<span class="default">(<font color="Maroon" title="c2">n</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">SQ2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:68"><span class="lab"><font color="Green" title="E36">BB3</font></span></a>, <a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E33">B11</font></span></a>, <a class="txt" href="fomodel4.html#E32"><span class="lab"><font color="Green" title="E27">Lm15b</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:68"/>
<font color="Maroon" title="c3">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="funct_7.html#K9" title="FUNCT_7:func.9">iter</a> (<span class="p2">(<span class="default"><a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">D2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">SQ1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:68"><span class="lab"><font color="Green" title="E38">B5</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</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>
