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<b>let </b><font color="Maroon" title="c1">IAlph</font>, <font color="Maroon" title="c2">OAlph</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">tfsm</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="c1">IAlph</font>,<font color="Maroon" title="c2">OAlph</font><br/> for <font color="Olive" title="b2">qa</font>, <font color="Olive" title="b3">qb</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b1">tfsm</font><br/> for <font color="Olive" title="b4">k</font>, <font color="Olive" title="b5">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b4">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b5">m</font> <a href="fsm_1.html#R6" title="FSM_1:pred.6">-equivalent</a> <font color="Olive" title="b2">qa</font>,<font color="Olive" title="b3">qb</font> holds <br/><font color="Olive" title="b4">k</font> <a href="fsm_1.html#R6" title="FSM_1:pred.6">-equivalent</a> <font color="Olive" title="b2">qa</font>,<font color="Olive" title="b3">qb</font></span><br/><b>let </b><font color="Maroon" title="c3">tfsm</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="c1">IAlph</font>,<font color="Maroon" title="c2">OAlph</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">qa</font>, <font color="Olive" title="b2">qb</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm</font><br/> for <font color="Olive" title="b3">k</font>, <font color="Olive" title="b4">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b3">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b4">m</font> <a href="fsm_1.html#R6" title="FSM_1:pred.6">-equivalent</a> <font color="Olive" title="b1">qa</font>,<font color="Olive" title="b2">qb</font> holds <br/><font color="Olive" title="b3">k</font> <a href="fsm_1.html#R6" title="FSM_1:pred.6">-equivalent</a> <font color="Olive" title="b1">qa</font>,<font color="Olive" title="b2">qb</font></span><br/><b>let </b><font color="Maroon" title="c4">qa</font>, <font color="Maroon" title="c5">qb</font> be   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">m</font> <a href="fsm_1.html#R6" title="FSM_1:pred.6">-equivalent</a> <font color="Maroon" title="c4">qa</font>,<font color="Maroon" title="c5">qb</font> holds <br/><font color="Olive" title="b1">k</font> <a href="fsm_1.html#R6" title="FSM_1:pred.6">-equivalent</a> <font color="Maroon" title="c4">qa</font>,<font color="Maroon" title="c5">qb</font></span><br/><b>let </b><font color="Maroon" title="c6">k</font>, <font color="Maroon" title="c7">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">m</font> <a href="fsm_1.html#R6" title="FSM_1:pred.6">-equivalent</a> <font color="Maroon" title="c4">qa</font>,<font color="Maroon" title="c5">qb</font> implies <font color="Maroon" title="c6">k</font> <a href="fsm_1.html#R6" title="FSM_1:pred.6">-equivalent</a> <font color="Maroon" title="c4">qa</font>,<font color="Maroon" title="c5">qb</font> )</span><br/>











<b>assume </b><a NAME="E1:55"/><i><font color="Green" title="E39">A1</font></i>: 
<font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">m</font> <a href="fsm_1.html#R6" title="FSM_1:pred.6">-equivalent</a> <font color="Maroon" title="c4">qa</font>,<font color="Maroon" title="c5">qb</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">k</font> <a href="fsm_1.html#R6" title="FSM_1:pred.6">-equivalent</a> <font color="Maroon" title="c4">qa</font>,<font color="Maroon" title="c5">qb</font></span><br/>

<a NAME="E2:55"/><i><font color="Green" title="E40">A2</font></i>: 
<font color="Maroon" title="c6">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">m</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<b>let </b><font color="Maroon" title="c8">w</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">IAlph</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="fsm_1.html#D11" target="_self" title="FSM_1:def.11">FSM_1:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">w</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> implies <font color="Maroon" title="c4">qa</font>,<font color="Maroon" title="c8">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="c5">qb</font>,<font color="Maroon" title="c8">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  )</span><br/>

<b>assume </b><a NAME="E3:55"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">w</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">qa</font>,<font color="Maroon" title="c8">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="c5">qb</font>,<font color="Maroon" title="c8">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span><br/>

<a NAME="E4:55"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">w</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">m</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E2:55"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E5:55"/>
<font color="Maroon" title="c4">qa</font>,<font color="Maroon" title="c8">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="c5">qb</font>,<font color="Maroon" title="c8">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:55"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="fsm_1.html#D11" target="_self" title="FSM_1:def.11">Def11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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