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<span class="kw">let </span><font color="Maroon" title="c1">OAlph</font>, <font color="Maroon" title="c2">IAlph</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">tfsm1</font>, <font color="Olive" title="b2">tfsm2</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_1.html#L2" title="FSM_1:struct.2">Mealy-FSM</a> of <font color="Maroon" title="c2">IAlph</font>,<font color="Maroon" title="c1">OAlph</font><br/>  for <font color="Olive" title="b3">q11</font>, <font color="Olive" title="b4">q12</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b1">tfsm1</font><br/>  for <font color="Olive" title="b5">Tf</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">tfsm1</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">tfsm2</font>  st (  for <font color="Olive" title="b6">q</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b1">tfsm1</font><br/>  for <font color="Olive" title="b7">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">IAlph</font> holds <br/> ( <font color="Olive" title="b5">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"> the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Olive" title="b1">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b6">q</font>,<font color="Olive" title="b7">s</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Olive" title="b2">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b5">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">q</font></span>)</span>,<font color="Olive" title="b7">s</font>) &amp;  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Olive" title="b1">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b6">q</font>,<font color="Olive" title="b7">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Olive" title="b2">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b5">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">q</font></span>)</span>,<font color="Olive" title="b7">s</font>) ) ) holds <br/>( <font color="Olive" title="b3">q11</font>,<font color="Olive" title="b4">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  iff <font color="Olive" title="b5">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">q11</font>,<font color="Olive" title="b5">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">tfsm1</font>, <font color="Maroon" title="c4">tfsm2</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_1.html#L2" title="FSM_1:struct.2">Mealy-FSM</a> of <font color="Maroon" title="c2">IAlph</font>,<font color="Maroon" title="c1">OAlph</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">q11</font>, <font color="Olive" title="b2">q12</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm1</font><br/>  for <font color="Olive" title="b3">Tf</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm1</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">tfsm2</font>  st (  for <font color="Olive" title="b4">q</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm1</font><br/>  for <font color="Olive" title="b5">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">IAlph</font> holds <br/> ( <font color="Olive" title="b3">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"> the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b5">s</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">q</font></span>)</span>,<font color="Olive" title="b5">s</font>) &amp;  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b5">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">q</font></span>)</span>,<font color="Olive" title="b5">s</font>) ) ) holds <br/>( <font color="Olive" title="b1">q11</font>,<font color="Olive" title="b2">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  iff <font color="Olive" title="b3">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q11</font>,<font color="Olive" title="b3">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">q11</font>, <font color="Maroon" title="c6">q12</font> be   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm1</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">Tf</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm1</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">tfsm2</font>  st (  for <font color="Olive" title="b2">q</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm1</font><br/>  for <font color="Olive" title="b3">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">IAlph</font> holds <br/> ( <font color="Olive" title="b1">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"> the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">s</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">q</font></span>)</span>,<font color="Olive" title="b3">s</font>) &amp;  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">q</font></span>)</span>,<font color="Olive" title="b3">s</font>) ) ) holds <br/>( <font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  iff <font color="Olive" title="b1">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q11</font>,<font color="Olive" title="b1">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c7">Tf</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm1</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">tfsm2</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">q</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm1</font><br/>  for <font color="Olive" title="b2">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">IAlph</font> holds <br/> ( <font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"> the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Olive" title="b2">s</font>) &amp;  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Olive" title="b2">s</font>) ) ) implies ( <font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  iff <font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  ) )</span><br/>













<span class="kw">set </span><font color="Maroon" title="c8">Stfsm1</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">Stfsm2</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">tfsm2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">OF1</font> =  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">tfsm1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">OF2</font> =  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font>;<br/>
<span class="kw">assume </span><a NAME="E1:71"/><span class="lab"><font color="Green" title="E52">A1</font></span>: 
 for <font color="Olive" title="b1">q</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm1</font><br/>  for <font color="Olive" title="b2">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">IAlph</font> holds <br/> ( <font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"> the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">s</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Olive" title="b2">s</font>) &amp;  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Olive" title="b2">s</font>) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  iff <font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  implies <font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  )</span>
<div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c12">Tq2</font> = <font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q12</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">tfsm2</font> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c13">Tq1</font> = <font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q11</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">tfsm2</font> ;<br/><span class="kw">assume </span><a NAME="E3:71_1"/><span class="lab"><font color="Green" title="E53">A2</font></span>: 
<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> </span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c14">w</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c2">IAlph</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (<font color="Maroon" title="c13">Tq1</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c12">Tq2</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span><br/><div><span class="lab"><font color="Green" title="E54">A3</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c15">k</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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c15">k</font> &amp; <font color="Maroon" title="c15">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c13">Tq1</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> implies <span class="p1">(<span class="default">(<font color="Maroon" title="c13">Tq1</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c12">Tq2</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:71_1_1_1"/><span class="lab"><font color="Green" title="E55">A4</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c15">k</font>
 <span class="kw">and </span><br/><a NAME="E2:71_1_1_1"/><span class="lab"><font color="Green" title="E56">A5</font></span>: 
<font color="Maroon" title="c15">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c13">Tq1</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">(<font color="Maroon" title="c13">Tq1</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c12">Tq2</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font></span><br/><a NAME="E3:71_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c13">Tq1</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">w</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>;<br/><a NAME="E4:71_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A6</font></span>: 
<font color="Maroon" title="c15">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">w</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71_1_1_1"><span class="lab"><font color="Green" title="E55">A4</font></span></a>, <a class="txt" href="#E2:71_1_1_1"><span class="lab"><font color="Green" title="E56">A5</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/><a NAME="E5:71_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A7</font></span>: 
<font color="Maroon" title="c15">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T8" title="FINSEQ_2:th.8">FINSEQ_2:8</a></span>;<br/><a NAME="E6:71_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A8</font></span>: 
<font color="Maroon" title="c15">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/><a NAME="E7:71_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>;<br/><a NAME="E8:71_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_1_1_1"><span class="lab"><font color="Green" title="E58">A7</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c16">q1a</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/><a NAME="E10:71_1_1_1"/><span class="lab"><font color="Green" title="E60">A9</font></span>: 
<font color="Maroon" title="c15">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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/><a NAME="E11:71_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>;<br/><a NAME="E12:71_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_1_1_1"><span class="lab"><font color="Green" title="E58">A7</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">q2a</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/><a NAME="E14:71_1_1_1"/><span class="lab"><font color="Green" title="E61">A10</font></span>: 
<font color="Maroon" title="c15">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:71_1_1_1"><span class="lab"><font color="Green" title="E57">A6</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c18">wk</font> = <font color="Maroon" title="c14">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">IAlph</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default">(<font color="Maroon" title="c13">Tq1</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font> = 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c13">Tq1</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:71_1_1_1"><span class="lab"><font color="Green" title="E61">A10</font></span></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">q1a</font></span>)</span>,<font color="Maroon" title="c18">wk</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="txt" href="#E1:71_1_1_1"><span class="lab"><font color="Green" title="E55">A4</font></span></a>, <a class="txt" href="#E6:71_1_1_1"><span class="lab"><font color="Green" title="E59">A8</font></span></a>, <a class="txt" href="#E10:71_1_1_1"><span class="lab"><font color="Green" title="E60">A9</font></span></a>, <a class="ref" href="fsm_1.html#T43" target="_self" title="FSM_1:th.43">Th60</a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c16">q1a</font>,<font color="Maroon" title="c18">wk</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E52">A1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:71_1_1_1"><span class="lab"><font color="Green" title="E61">A10</font></span></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:71_1"><span class="lab"><font color="Green" title="E53">A2</font></span></a>, <a class="ref" href="fsm_1.html#D10" target="_self" title="FSM_1:def.10">Def10</a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c17">q2a</font>,<font color="Maroon" title="c18">wk</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:71_1_1_1"><span class="lab"><font color="Green" title="E61">A10</font></span></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">q2a</font></span>)</span>,<font color="Maroon" title="c18">wk</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E52">A1</font></span></a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c12">Tq2</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="txt" href="#E1:71_1_1_1"><span class="lab"><font color="Green" title="E55">A4</font></span></a>, <a class="txt" href="#E6:71_1_1_1"><span class="lab"><font color="Green" title="E59">A8</font></span></a>, <a class="txt" href="#E10:71_1_1_1"><span class="lab"><font color="Green" title="E60">A9</font></span></a>, <a class="ref" href="fsm_1.html#T43" target="_self" title="FSM_1:th.43">Th60</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c12">Tq2</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:71_1_1_1"><span class="lab"><font color="Green" title="E61">A10</font></span></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</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 href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c13">Tq1</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">w</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c12">Tq2</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:71_1_1"/>
(<font color="Maroon" title="c13">Tq1</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c12">Tq2</font>,<font color="Maroon" title="c14">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71_1_1"><span class="lab"><font color="Green" title="E54">A3</font></span></a>, <a class="ref" href="finseq_1.html#T14" title="FINSEQ_1:th.14">FINSEQ_1:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:71_1"/>
<font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D10" target="_self" title="FSM_1:def.10">Def10</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>

<span class="kw">assume </span><a NAME="E3:71"/><span class="lab"><font color="Green" title="E53">A11</font></span>: 
<font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">w</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c2">IAlph</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span><br/><div><span class="lab"><font color="Green" title="E54">A12</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="71_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c13">k</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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> implies <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:71_2_1"/><span class="lab"><font color="Green" title="E55">A13</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font>
 <span class="kw">and </span><br/><a NAME="E2:71_2_1"/><span class="lab"><font color="Green" title="E56">A14</font></span>: 
<font color="Maroon" title="c13">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span><br/><a NAME="E3:71_2_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">w</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>;<br/><a NAME="E4:71_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A15</font></span>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">w</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71_2_1"><span class="lab"><font color="Green" title="E55">A13</font></span></a>, <a class="txt" href="#E2:71_2_1"><span class="lab"><font color="Green" title="E56">A14</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/><a NAME="E5:71_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A16</font></span>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T8" title="FINSEQ_2:th.8">FINSEQ_2:8</a></span>;<br/><a NAME="E6:71_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A17</font></span>: 
( <font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp; <font color="Maroon" title="c13">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/><a NAME="E7:71_2_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>;<br/><a NAME="E8:71_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_2_1"><span class="lab"><font color="Green" title="E58">A16</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">q2a</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/><a NAME="E10:71_2_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>;<br/><a NAME="E11:71_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:71_2_1"><span class="lab"><font color="Green" title="E58">A16</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">q1a</font> = <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/><a NAME="E13:71_2_1"/><span class="lab"><font color="Green" title="E60">A18</font></span>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c12">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:71_2_1"><span class="lab"><font color="Green" title="E57">A15</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c16">wk</font> = <font color="Maroon" title="c12">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">IAlph</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> = 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:71_2_1"><span class="lab"><font color="Green" title="E60">A18</font></span></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">q1a</font></span>)</span>,<font color="Maroon" title="c16">wk</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E52">A1</font></span></a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><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="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q11</font></span>)</span>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span>,<font color="Maroon" title="c16">wk</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="txt" href="#E1:71_2_1"><span class="lab"><font color="Green" title="E55">A13</font></span></a>, <a class="txt" href="#E6:71_2_1"><span class="lab"><font color="Green" title="E59">A17</font></span></a>, <a class="ref" href="fsm_1.html#T43" target="_self" title="FSM_1:th.43">Th60</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q11</font></span>)</span>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:71_2_1"><span class="lab"><font color="Green" title="E60">A18</font></span></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
<br/>.= 
<span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q12</font></span>)</span>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:71"><span class="lab"><font color="Green" title="E53">A11</font></span></a>, <a class="ref" href="fsm_1.html#D10" target="_self" title="FSM_1:def.10">Def10</a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><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="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q12</font></span>)</span>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:71_2_1"><span class="lab"><font color="Green" title="E60">A18</font></span></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">q2a</font></span>)</span>,<font color="Maroon" title="c16">wk</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E52">A1</font></span></a>, <a class="txt" href="#E1:71_2_1"><span class="lab"><font color="Green" title="E55">A13</font></span></a>, <a class="txt" href="#E6:71_2_1"><span class="lab"><font color="Green" title="E59">A17</font></span></a>, <a class="ref" href="fsm_1.html#T43" target="_self" title="FSM_1:th.43">Th60</a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">tfsm1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c14">q2a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E52">A1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default">(<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:71_2_1"><span class="lab"><font color="Green" title="E60">A18</font></span></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</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 href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">w</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:71_2"/>
(<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c6">q12</font>,<font color="Maroon" title="c12">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71_2"><span class="lab"><font color="Green" title="E54">A12</font></span></a>, <a class="ref" href="finseq_1.html#T14" title="FINSEQ_1:th.14">FINSEQ_1:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:71"/>
<font color="Maroon" title="c5">q11</font>,<font color="Maroon" title="c6">q12</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D10" target="_self" title="FSM_1:def.10">Def10</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>
