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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">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b4">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b5">D1</font>, <font color="Olive" title="b6">D2</font>, <font color="Olive" title="b7">D3</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Olive" title="b4">S</font><br/>  for <font color="Olive" title="b8">SQ1</font>, <font color="Olive" title="b9">SQ2</font> being  <font color="Olive">b<sub>4</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="b5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b6">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <span class="p1">(<span class="default"><font color="Olive" title="b5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b6">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b7">D3</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Olive" title="b1">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Olive" title="b8">SQ1</font>,<font color="Olive" title="b5">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  &amp; <font color="Olive" title="b2">y</font> is <font color="Maroon" title="c1">m</font>,<font color="Olive" title="b9">SQ2</font>,<font color="Olive" title="b6">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  &amp; <font color="Olive" title="b3">z</font> is <font color="Maroon" title="c2">n</font>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Olive" title="b7">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  holds <br/><font color="Olive" title="b3">z</font> is <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>,<font color="Olive" title="b8">SQ1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b9">SQ2</font>,<span class="p1">(<span class="default"><font color="Olive" title="b5">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b6">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b7">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</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="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>, <font color="Olive" title="b4">D3</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="b5">SQ1</font>, <font color="Olive" title="b6">SQ2</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> <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; <span class="p1">(<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> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b4">D3</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Maroon" title="c3">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Olive" title="b5">SQ1</font>,<font color="Olive" title="b2">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  &amp; <font color="Maroon" title="c4">y</font> is <font color="Maroon" title="c1">m</font>,<font color="Olive" title="b6">SQ2</font>,<font color="Olive" title="b3">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  &amp; <font color="Maroon" title="c5">z</font> is <font color="Maroon" title="c2">n</font>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Olive" title="b4">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  holds <br/><font color="Maroon" title="c5">z</font> is <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>,<font color="Olive" title="b5">SQ1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b6">SQ2</font>,<span class="p1">(<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> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b4">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">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>, <font color="Olive" title="b3">D3</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c6">S</font><br/>  for <font color="Olive" title="b4">SQ1</font>, <font color="Olive" title="b5">SQ2</font> being  <font color="Maroon" title="c6">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> <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; <span class="p1">(<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> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">D3</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Maroon" title="c3">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Olive" title="b4">SQ1</font>,<font color="Olive" title="b1">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  &amp; <font color="Maroon" title="c4">y</font> is <font color="Maroon" title="c1">m</font>,<font color="Olive" title="b5">SQ2</font>,<font color="Olive" title="b2">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  &amp; <font color="Maroon" title="c5">z</font> is <font color="Maroon" title="c2">n</font>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Olive" title="b3">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  holds <br/><font color="Maroon" title="c5">z</font> is <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>,<font color="Olive" title="b4">SQ1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b5">SQ2</font>,<span class="p1">(<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> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c7">D1</font>, <font color="Maroon" title="c8">D2</font>, <font color="Maroon" title="c9">D3</font> be   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Maroon" title="c6">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">SQ1</font>, <font color="Olive" title="b2">SQ2</font> being  <font color="Maroon" title="c6">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="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Maroon" title="c3">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Olive" title="b1">SQ1</font>,<font color="Maroon" title="c7">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  &amp; <font color="Maroon" title="c4">y</font> is <font color="Maroon" title="c1">m</font>,<font color="Olive" title="b2">SQ2</font>,<font color="Maroon" title="c8">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  &amp; <font color="Maroon" title="c5">z</font> is <font color="Maroon" title="c2">n</font>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c9">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  holds <br/><font color="Maroon" title="c5">z</font> is <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>,<font color="Olive" title="b1">SQ1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">SQ2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c10">SQ1</font>, <font color="Maroon" title="c11">SQ2</font> be  <font color="Maroon" title="c6">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="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <font color="Maroon" title="c3">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c10">SQ1</font>,<font color="Maroon" title="c7">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  &amp; <font color="Maroon" title="c4">y</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c11">SQ2</font>,<font color="Maroon" title="c8">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  &amp; <font color="Maroon" title="c5">z</font> is <font color="Maroon" title="c2">n</font>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c9">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  implies <font color="Maroon" title="c5">z</font> is <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>,<font color="Maroon" title="c10">SQ1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c11">SQ2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  )</span><br/>





















<span class="kw">set </span><font color="Maroon" title="c12">Q</font> = <font color="Maroon" title="c6">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">D</font> = <font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">O1</font> =  <a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c7">D1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">O2</font> =  <a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c8">D2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">O3</font> =  <a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <font color="Maroon" title="c9">D3</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">O</font> =  <a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">OO</font> =  <a href="fomodel4.html#K2" title="FOMODEL4:func.2">OneStep</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</font></span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c19">X</font> = <font color="Maroon" title="c10">SQ1</font>, <font color="Maroon" title="c20">Y</font> = <font color="Maroon" title="c11">SQ2</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="fomodel4.html#K1" title="FOMODEL4:func.1">-sequents</a></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D3" target="_self" title="FOMODEL4:def.3">DefSeqtLike2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">Z</font> = <font color="Maroon" title="c19">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c20">Y</font>;<br/>
<span class="kw">assume </span><a NAME="E2:130"/><span class="lab"><font color="Green" title="E89">B1</font></span>: 
( <font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font> is  <a href="fomodel4.html#V6" title="FOMODEL4:attr.6">isotone</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</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="c3">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c10">SQ1</font>,<font color="Maroon" title="c7">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  or  not <font color="Maroon" title="c4">y</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c11">SQ2</font>,<font color="Maroon" title="c8">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  or  not <font color="Maroon" title="c5">z</font> is <font color="Maroon" title="c2">n</font>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c9">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  or <font color="Maroon" title="c5">z</font> is <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>,<font color="Maroon" title="c10">SQ1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c11">SQ2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E3:130"/><span class="lab"><font color="Green" title="E90">B3</font></span>: 
( <font color="Maroon" title="c3">x</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c10">SQ1</font>,<font color="Maroon" title="c7">D1</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  &amp; <font color="Maroon" title="c4">y</font> is <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c11">SQ2</font>,<font color="Maroon" title="c8">D2</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</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="c5">z</font> is <font color="Maroon" title="c2">n</font>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c9">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  or <font color="Maroon" title="c5">z</font> is <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>,<font color="Maroon" title="c10">SQ1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c11">SQ2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a>  )</span><br/>

<a NAME="E4:130"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">BB2</font></span>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c7">D1</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">X</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c8">D2</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">Y</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D7" target="_self" title="FOMODEL4:def.7">DefDerivable3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c22">sq1</font> = <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c23">sq2</font> = <font color="Maroon" title="c4">y</font> as  <font color="Maroon" title="c6">S</font> <a href="fomodel4.html#V1" title="FOMODEL4:attr.1">-sequent-like</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:130"><span class="lab"><font color="Green" title="E90">B3</font></span></a></span>;<br/>
<a NAME="E6:130"/>
( <font color="Maroon" title="c19">X</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <font color="Maroon" title="c20">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c20">Y</font> &amp; <font color="Maroon" title="c20">Y</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <font color="Maroon" title="c19">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c19">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c20">Y</font> &amp; <font color="Maroon" title="c7">D1</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <font color="Maroon" title="c8">D2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font> &amp; <font color="Maroon" title="c8">D2</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <font color="Maroon" title="c7">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font> )
 
;<br/>
<a NAME="E7:130"/><span class="kw">then </span>
( <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c7">D1</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">X</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="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c20">Y</font></span>)</span> &amp; <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c8">D2</font>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">Y</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="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c20">Y</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel4.html#E31"><span class="lab"><font color="Green" title="E26">Lm15</font></span></a>, <a class="txt" href="#E2:130"><span class="lab"><font color="Green" title="E89">B1</font></span></a></span>;<br/>
<a NAME="E8:130"/><span class="kw">then </span><span class="lab"><font color="Green" title="E92">B0</font></span>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c22">sq1</font>,<font color="Maroon" title="c23">sq2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <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="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">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> <span class="p1">(<span class="default"><font color="Maroon" title="c19">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c20">Y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:130"><span class="lab"><font color="Green" title="E91">BB2</font></span></a>, <a class="ref" href="zfmisc_1.html#T32" title="ZFMISC_1:th.32">ZFMISC_1:32</a></span>;<br/>
<span class="kw">assume </span><a NAME="E9:130"/>
<font color="Maroon" title="c5">z</font> is <font color="Maroon" title="c2">n</font>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<font color="Maroon" title="c9">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</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">z</font> is <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>,<font color="Maroon" title="c10">SQ1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c11">SQ2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> </span><br/>

<a NAME="E10:130"/><span class="kw">then </span>
<font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c9">D3</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> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D7" target="_self" title="FOMODEL4:def.7">DefDerivable3</a></span>;<br/>
<a NAME="E11:130"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">z</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <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="c9">D3</font></span>)</span>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T31" title="ZFMISC_1:th.31">ZFMISC_1:31</a></span>;<br/>
<a NAME="E12:130"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">z</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <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"><span class="p4">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</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> <span class="p1">(<span class="default"><font color="Maroon" title="c19">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c20">Y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:130"><span class="lab"><font color="Green" title="E92">B0</font></span></a>, <a class="txt" href="#E2:130"><span class="lab"><font color="Green" title="E89">B1</font></span></a>, <a class="txt" href="fomodel4.html#E37"><span class="lab"><font color="Green" title="E32">Lm27</font></span></a></span>;<br/>
<a NAME="E13:130"/><span class="kw">then </span>
<font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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"><span class="p3">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</font></span>)</span>) <a href="fomodel4.html#K3" title="FOMODEL4:func.3">-derivables</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c20">Y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T31" title="ZFMISC_1:th.31">ZFMISC_1:31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:130"/>
<font color="Maroon" title="c5">z</font> is <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>,<font color="Maroon" title="c10">SQ1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c11">SQ2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">D1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c8">D2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">D3</font> <a href="fomodel4.html#V4" title="FOMODEL4:attr.4">-derivable</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel4.html#D7" target="_self" title="FOMODEL4:def.7">DefDerivable3</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>
