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<span class="kw">let </span><font color="Maroon" title="c1">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">  for <font color="Olive" title="b1">U</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b2">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/>  for <font color="Olive" title="b3">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b4">l</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Olive" title="b3">S</font><br/>  for <font color="Olive" title="b5">I</font> being  <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b6">tt0</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Olive" title="b3">S</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default">(<font color="Olive" title="b4">l</font>,<font color="Olive" title="b6">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p5">(<span class="default">(<font color="Olive" title="b3">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Olive" title="b6">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">n</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default">(<font color="Olive" title="b4">l</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive" title="b5">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b5">I</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b5">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">tt0</font></span>)</span>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">n</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">U</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">  for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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">l</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b4">I</font> being  <font color="Olive">b<sub>2</sub></font>,<font color="Maroon" title="c2">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b5">tt0</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Olive" title="b2">S</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default">(<font color="Olive" title="b3">l</font>,<font color="Olive" title="b5">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p5">(<span class="default">(<font color="Olive" title="b2">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Olive" title="b5">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default">(<font color="Olive" title="b3">l</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive" title="b4">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b4">I</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b4">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">tt0</font></span>)</span>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">n</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">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">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b2">l</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">I</font> being  <font color="Olive">b<sub>1</sub></font>,<font color="Maroon" title="c2">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b4">tt0</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Olive" title="b1">S</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default">(<font color="Olive" title="b2">l</font>,<font color="Olive" title="b4">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p5">(<span class="default">(<font color="Olive" title="b1">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Olive" title="b4">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default">(<font color="Olive" title="b2">l</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive" title="b3">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b3">I</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b3">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">tt0</font></span>)</span>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span></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">l</font> being   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</a> of <font color="Maroon" title="c4">S</font><br/>  for <font color="Olive" title="b2">I</font> being  <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c2">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b3">tt0</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default">(<font color="Olive" title="b1">l</font>,<font color="Olive" title="b3">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p5">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Olive" title="b3">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default">(<font color="Olive" title="b1">l</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive" title="b2">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b2">I</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b2">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">tt0</font></span>)</span>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">l</font> be   <a href="fomodel1.html#V4" title="FOMODEL1:attr.4">literal</a>  <a href="fomodel1.html#NM1" title="FOMODEL1:NM.1">Element</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">I</font> being  <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c2">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b2">tt0</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Olive" title="b2">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p5">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Olive" title="b2">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive" title="b1">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Olive" title="b1">I</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">tt0</font></span>)</span>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">I</font> be  <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c2">U</font> <a href="fomodel2.html#V1" title="FOMODEL2:attr.1">-interpreter-like</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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">tt0</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Olive" title="b1">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p5">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Olive" title="b1">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">tt0</font></span>)</span>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">tt0</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p5">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span><br/>













<span class="kw">set </span><font color="Maroon" title="c8">II</font> = <font color="Maroon" title="c2">U</font> <a href="fomodel2.html#K16" title="FOMODEL2:func.16">-InterpretersOf</a> <font color="Maroon" title="c4">S</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">u</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">U</font> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">F</font> = <font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">FI</font> = (<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">H</font> = (<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">TT</font> =  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">TI</font> = (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">TF</font> = (<span class="p1">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">TH</font> = (<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">TII</font> = <font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">J</font> = (<font color="Maroon" title="c5">l</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">TJ</font> = (<span class="p1">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">C</font> = <font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K21" title="FOMODEL1:func.21">-multiCat</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">SS</font> =  <a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c4">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c22">T</font> = <font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c23">t0</font> = <font color="Maroon" title="c7">tt0</font> as   <a href="fomodel1.html#V13" title="FOMODEL1:attr.13">termal</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c4">S</font> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c24">k</font> =  <a href="fomodel1.html#K38" title="FOMODEL1:func.38">Depth</a> <font color="Maroon" title="c23">t0</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c25">t00</font> = <font color="Maroon" title="c23">t0</font> as   <a href="fomodel1.html#K38" title="FOMODEL1:func.38">Depth</a> <font color="Maroon" title="c23">t0</font> <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c4">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D40" title="FOMODEL1:def.40">FOMODEL1:def 40</a></span>;<br/>
<a NAME="E4:116"/><span class="lab"><font color="Green" title="E48">B3</font></span>: 
( <font color="Maroon" title="c5">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">l</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c7">tt0</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">l</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">l</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E5:116"/><span class="kw">then </span>
( <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c7">tt0</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">l</font> &amp; <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">l</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>;<br/>
<a NAME="E6:116"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">B2</font></span>: 
( <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c7">tt0</font> &amp; <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:116"><span class="lab"><font color="Green" title="E48">B3</font></span></a>, <a class="ref" href="funcop_1.html#T7" title="FUNCOP_1:th.7">FUNCOP_1:7</a></span>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p5">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> $1</span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> $1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> $1</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> $1</span>)</span>;<br/>
<a NAME="E7:116"/><span class="lab"><font color="Green" title="E50">B0</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="116_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:116_1"/><span class="lab"><font color="Green" title="E51">C0</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c9">u</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c7">tt0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E2:116_1"/>
( <span class="p1">(<span class="default">(<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c9">u</font> &amp; <span class="p1">(<span class="default">(<span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c7">tt0</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D8" title="FOMODEL2:def.8">FOMODEL2:def 8</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p4">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:116_1"><span class="lab"><font color="Green" title="E51">C0</font></span></a>, <a class="ref" href="funcop_1.html#T17" title="FUNCOP_1:th.17">FUNCOP_1:17</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#D8" title="FOMODEL2:def.8">FOMODEL2:def 8</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:116_1"/>
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 ; <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>
<a NAME="E8:116"/><span class="lab"><font color="Green" title="E51">B1</font></span>: 
 for <font color="Olive" title="b1">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="116_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c26">m</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"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c26">m</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c26">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c27">mm</font> = <font color="Maroon" title="c26">m</font>, <font color="Maroon" title="c28">MM</font> = <font color="Maroon" title="c26">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 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">assume </span><a NAME="E2:116_2"/><span class="lab"><font color="Green" title="E52">C2</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c26">m</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">S<sub>1</sub></font>[<font color="Maroon" title="c26">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c29">TM</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c28">MM</font>, <font color="Maroon" title="c30">Tm</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c27">mm</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#T2" title="FOMODEL1:th.2">FOMODEL1:2</a></span>;<br/>
<a NAME="E4:116_2"/>
( <span class="p1">(<span class="default">(<span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c27">mm</font> is    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>,<font color="Maroon" title="c2">U</font>) &amp; <span class="p1">(<span class="default">(<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c28">MM</font> is    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>,<font color="Maroon" title="c2">U</font>) &amp; <span class="p1">(<span class="default">(<span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c28">MM</font> is    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>,<font color="Maroon" title="c2">U</font>) &amp; <span class="p1">(<span class="default">(<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c27">mm</font> is    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>,<font color="Maroon" title="c2">U</font>) )
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c31">Jm</font> = <span class="p1">(<span class="default">(<span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c27">mm</font>, <font color="Maroon" title="c32">JM</font> = <span class="p1">(<span class="default">(<span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c28">MM</font>, <font color="Maroon" title="c33">IM</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c28">MM</font>, <font color="Maroon" title="c34">Imm</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c27">mm</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>,<font color="Maroon" title="c2">U</font> ;<br/>
<a NAME="E6:116_2"/>
( <span class="p1">(<span class="default">(<span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c27">mm</font> is    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>) &amp; <span class="p1">(<span class="default">(<span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c28">MM</font> is    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>) )
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c35">Hm</font> = <span class="p1">(<span class="default">(<span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c27">mm</font>, <font color="Maroon" title="c36">HM</font> = <span class="p1">(<span class="default">(<span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c28">MM</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>,<span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c37">LH</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c38">RH</font> = <font color="Maroon" title="c32">JM</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font>;<br/>
<a NAME="E8:116_2"/><span class="lab"><font color="Green" title="E53">C0</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">TM</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">JM</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">TM</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="116_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c39">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="c39">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</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#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">JM</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <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="E1:116_2_1"/><span class="lab"><font color="Green" title="E54">D5</font></span>: 
<font color="Maroon" title="c39">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</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#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">JM</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><a NAME="E2:116_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c39">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T57" title="RELAT_1:th.57">RELAT_1:57</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c40">tt</font> = <font color="Maroon" title="c39">x</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c41">t</font> = <font color="Maroon" title="c39">x</font> as  <font color="Maroon" title="c27">mm</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c4">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:116_2"><span class="lab"><font color="Green" title="E53">C0</font></span></a>, <a class="txt" href="#E1:116_2_1"><span class="lab"><font color="Green" title="E54">D5</font></span></a>, <a class="ref" href="fomodel1.html#D33" title="FOMODEL1:def.33">FOMODEL1:def 33</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c42">ttt</font> = <font color="Maroon" title="c39">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c29">TM</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:116_2_1"><span class="lab"><font color="Green" title="E54">D5</font></span></a>, <a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c43">ST</font> =  <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c41">t</font>;<br/><span class="kw">set </span><font color="Maroon" title="c44">o</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font>;<br/><span class="kw">set </span><font color="Maroon" title="c45">n</font> =  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span>;<br/><a NAME="E6:116_2_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c33">IM</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c42">ttt</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c33">IM</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c42">ttt</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c32">JM</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c42">ttt</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">JM</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c42">ttt</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c42">ttt</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c42">ttt</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/><a NAME="E7:116_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">D7</font></span>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c33">IM</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c33">IM</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c32">JM</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">JM</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">x</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">x</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/><a NAME="E8:116_2_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c33">IM</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c40">tt</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c33">IM</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c36">HM</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c40">tt</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c40">tt</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c36">HM</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c40">tt</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/><a NAME="E9:116_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">C1</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c33">IM</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c33">IM</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">HM</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c41">t</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c40">tt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</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="c36">HM</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c40">tt</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c46">newterms</font> = <font color="Maroon" title="c35">Hm</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c41">t</font></span>)</span> as   <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T26" title="FOMODEL0:th.26">FOMODEL0:26</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c47">newtermss</font> = <font color="Maroon" title="c46">newterms</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T16" title="FOMODEL0:th.16">FOMODEL0:16</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c48">newtermsss</font> = <font color="Maroon" title="c46">newterms</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Maroon" title="c4">S</font></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T26" title="FOMODEL0:th.26">FOMODEL0:26</a></span>;<br/><a NAME="E13:116_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p5">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p4">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c47">newtermss</font></span>)</span> <a href="xboole_0.html#K5" title="XBOOLE_0:func.5">\+\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c47">newtermss</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><a NAME="E14:116_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">D0</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p4">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c46">newterms</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c46">newterms</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T29" title="FOMODEL0:th.29">FOMODEL0:29</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="116_2_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="E1:116_2_1_1"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</font> or <span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">l</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="116_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:116_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</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#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">JM</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <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="E2:116_2_1_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</font> &amp; <font color="Maroon" title="c41">t</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#T16" title="FOMODEL1:th.16">FOMODEL1:16</a></span>;<br/><a NAME="E3:116_2_1_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</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="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c7">tt0</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span> &amp; <font color="Maroon" title="c32">JM</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:116_2_1"><span class="lab"><font color="Green" title="E56">C1</font></span></a>, <a class="txt" href="#E6:116"><span class="lab"><font color="Green" title="E49">B2</font></span></a>, <a class="ref" href="fomodel2.html#T3" title="FOMODEL2:th.3">FOMODEL2:3</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E4:116_2_1_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font> &amp; <font color="Maroon" title="c32">JM</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T7" title="FUNCOP_1:th.7">FUNCOP_1:7</a></span>;<br/><span class="kw">hence </span><a NAME="E5:116_2_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">JM</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:116_2_1"><span class="lab"><font color="Green" title="E55">D7</font></span></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="116_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:116_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">l</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</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#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">JM</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <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="E2:116_2_1_1_2"/><span class="kw">then </span>
 not <span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">l</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E3:116_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">D5</font></span>: 
(  not <span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c7">tt0</font></span>)</span></span>)</span> &amp;  not <span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/><a NAME="E4:116_2_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">XX</font></span>: <span class="p1">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span> = 
<font color="Maroon" title="c1">X</font> <a href="fomodel3.html#K4" title="FOMODEL3:func.4">-freeInterpreter</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel3.html#D4" target="_self" title="FOMODEL3:def.4">DefFree1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span> <a href="fomodel3.html#K2" title="FOMODEL3:func.2">-compound</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel3.html#D3" target="_self" title="FOMODEL3:def.3">DefFreeInt1</a></span>
;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c49">newtermssss</font> = <font color="Maroon" title="c46">newterms</font> as   <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K19" title="FOMODEL1:func.19">ar</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span> <a href="fomodel0.html#K2" title="FOMODEL0:func.2">*</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></span>;<br/><a NAME="E7:116_2_1_1_2"/><span class="lab"><font color="Green" title="E60">D1</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c46">newterms</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span> <a href="fomodel3.html#K1" title="FOMODEL3:func.1">-compound</a> <font color="Maroon" title="c49">newtermssss</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:116_2_1"><span class="lab"><font color="Green" title="E57">D0</font></span></a>, <a class="ref" href="fomodel3.html#D2" target="_self" title="FOMODEL3:def.2">DefCompound1</a>, <a class="txt" href="#E5:116_2_1_1_2"><span class="lab"><font color="Green" title="E59">XX</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c50">t1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span> <a href="fomodel3.html#K1" title="FOMODEL3:func.1">-compound</a> <font color="Maroon" title="c49">newtermssss</font> as   <a href="fomodel1.html#V13" title="FOMODEL1:attr.13">termal</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c4">S</font> ;<br/><span class="kw">set </span><font color="Maroon" title="c51">p</font> =  <a href="fomodel1.html#K38" title="FOMODEL1:func.38">Depth</a> <font color="Maroon" title="c50">t1</font>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c52">pp</font> =  <a href="fomodel1.html#K38" title="FOMODEL1:func.38">Depth</a> <font color="Maroon" title="c50">t1</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">reconsider </span><font color="Maroon" title="c53">t111</font> = <font color="Maroon" title="c50">t1</font> as   <a href="fomodel1.html#K38" title="FOMODEL1:func.38">Depth</a> <font color="Maroon" title="c50">t1</font> <a href="fomodel1.html#V14" title="FOMODEL1:attr.14">-termal</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Maroon" title="c4">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D40" title="FOMODEL1:def.40">FOMODEL1:def 40</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c54">t11</font> = <font color="Maroon" title="c50">t1</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D32" title="FOMODEL1:def.32">FOMODEL1:def 32</a></span>;<br/><a NAME="E12:116_2_1_1_2"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c52">pp</font> is    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>,<font color="Maroon" title="c2">U</font>)
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c55">Ip</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c9">u</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c52">pp</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="fomodel1.html#K35" title="FOMODEL1:func.35">AllTermsOf</a> <font color="Maroon" title="c4">S</font></span>)</span>,<font color="Maroon" title="c2">U</font> ;<br/><span class="lab"><font color="Green" title="E61">D2</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c50">t1</font> = 
<font color="Maroon" title="c50">t1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T6" title="FOMODEL0:th.6">FOMODEL0:6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T41" title="FINSEQ_1:th.41">FINSEQ_1:41</a></span>
;<br/><a NAME="E15:116_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">D3</font></span>: 
 <a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c50">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c49">newtermssss</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel1.html#D37" title="FOMODEL1:def.37">FOMODEL1:def 37</a></span>;<br/><a NAME="E16:116_2_1_1_2"/><span class="lab"><font color="Green" title="E63">Z6</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c35">Hm</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c30">Tm</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">Tm</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">Jm</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c30">Tm</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">Tm</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c41">t</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c30">Tm</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a>, <a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c41">t</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">t1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:116_2_1_1_2"><span class="lab"><font color="Green" title="E60">D1</font></span></a>, <a class="txt" href="#E9:116_2_1"><span class="lab"><font color="Green" title="E56">C1</font></span></a>, <a class="ref" href="fomodel2.html#T3" title="FOMODEL2:th.3">FOMODEL2:3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></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"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c50">t1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:116_2_1_1_2"><span class="lab"><font color="Green" title="E61">D2</font></span></a>, <a class="ref" href="fomodel2.html#T21" title="FOMODEL2:th.21">FOMODEL2:21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></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"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c35">Hm</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c30">Tm</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:116_2_1_1_2"><span class="lab"><font color="Green" title="E63">Z6</font></span></a>, <a class="txt" href="#E15:116_2_1_1_2"><span class="lab"><font color="Green" title="E62">D3</font></span></a>, <a class="ref" href="relat_1.html#T165" title="RELAT_1:th.165">RELAT_1:165</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></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"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c35">Hm</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c30">Tm</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T36" title="RELAT_1:th.36">RELAT_1:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</font></span>)</span></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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c35">Hm</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c30">Tm</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T83" title="RELAT_1:th.83">RELAT_1:83</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</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="c31">Jm</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:116_2"><span class="lab"><font color="Green" title="E52">C2</font></span></a>, <a class="txt" href="#E16:116_2_1_1_2"><span class="lab"><font color="Green" title="E63">Z6</font></span></a>, <a class="ref" href="relat_1.html#T165" title="RELAT_1:th.165">RELAT_1:165</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span> <a href="fomodel2.html#K4" title="FOMODEL2:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K22" title="FOMODEL1:func.22">-firstChar</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c41">t</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="c31">Jm</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K33" title="FOMODEL1:func.33">SubTerms</a> <font color="Maroon" title="c41">t</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:116_2_1_1_2"><span class="lab"><font color="Green" title="E58">D5</font></span></a>, <a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>
<br/>.= 
<font color="Maroon" title="c32">JM</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c41">t</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel2.html#T3" title="FOMODEL2:th.3">FOMODEL2:3</a></span>
;<br/><span class="kw">hence </span><a NAME="E18:116_2_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c36">HM</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c32">JM</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c29">TM</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:116_2_1"><span class="lab"><font color="Green" title="E55">D7</font></span></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">hence </span><a NAME="E10:116_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c26">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:116_2"><span class="lab"><font color="Green" title="E53">C0</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</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>
<a NAME="E9:116"/>
 for <font color="Olive" title="b1">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">m</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="#E7:116"><span class="lab"><font color="Green" title="E50">B0</font></span></a>, <a class="txt" href="#E8:116"><span class="lab"><font color="Green" title="E51">B1</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E10:116"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default">(<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K37" title="FOMODEL2:func.37">ReassignIn</a> <span class="p5">(<span class="default">(<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c1">X</font>) <a href="fomodel3.html#K7" title="FOMODEL3:func.7">-freeInterpreter</a></span>)</span></span>)</span>,<font color="Maroon" title="c7">tt0</font>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default">(<font color="Maroon" title="c5">l</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K5" title="FOMODEL2:func.5">ReassignIn</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">I</font> <a href="fomodel2.html#K10" title="FOMODEL2:func.10">-TermEval</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">tt0</font></span>)</span>) <a href="fomodel2.html#K8" title="FOMODEL2:func.8">-TermEval</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">S</font> <a href="fomodel1.html#K39" title="FOMODEL1:func.39">-termsOfMaxDepth</a></span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c3">n</font></span>)</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>
