reserve p for preProgram of SCM+FSA,
  ic for Instruction of SCM+FSA,
  i,j,k for Nat,
  fa,f for FinSeq-Location,
  a,b,da,db for Int-Location,
  la,lb for Nat;
reserve p1,p2,q for Instruction-Sequence of SCM+FSA;
reserve n for Nat;

theorem Th26:
  for p be Instruction-Sequence of SCM+FSA
  for s be State of SCM+FSA holds
  s.(fsloc 0), IExec(bubble-sort (fsloc 0),p,s).(fsloc 0)
  are_fiberwise_equipotent &
  for i,j be Nat st i>=1 & j<=len (s.(fsloc 0)) & i<j
  for x1,x2 be Integer st x1 =IExec(bubble-sort (fsloc 0),p,s).(fsloc 0).i &
  x2=IExec(bubble-sort (fsloc 0),p,s).(fsloc 0).j holds x1 >= x2
proof
  let p be Instruction-Sequence of SCM+FSA;
  let s be State of SCM+FSA;
  set W27=w2 ";" w3 ";" w4 ";" w5 ";" w6 ";" w7, s0=Initialized s,
  s1=Exec(w2, s0), s2=IExec(w2 ";" w3,p,s), s3=IExec(w2 ";" w3 ";" w4,p,s),
  s4=IExec(w2 ";" w3 ";" w4 ";" w5,p,s),
  s5=IExec(w2 ";" w3 ";" w4 ";" w5 ";" w6,p,s), s6=IExec(W27,p,s);
A1: s5.f0 =Exec(w6, s4).f0 by SCMFSA6C:7
    .=s4.f0 by SCMFSA_2:63
    .=Exec(w5, s3).f0 by SCMFSA6C:7
    .=s3.f0 by SCMFSA_2:63
    .=Exec(w4, s2).f0 by SCMFSA6C:7
    .=s2.f0 by SCMFSA_2:63
    .=Exec(w3, s1).f0 by SCMFSA6C:9
    .=s1.f0 by SCMFSA_2:63
    .=s0.f0 by SCMFSA_2:63
    .=s.f0 by SCMFSA_M:37;
A2: s6.f0 =Exec(w7, s5).f0 by SCMFSA6C:7
    .=s.f0 by A1,SCMFSA_2:74;
A3: s6.b1=Exec(w7, s5).b1 by SCMFSA6C:6
    .=len (s6.f0) by A1,A2,SCMFSA_2:74;
A4: IExec(bubble-sort f0,p,s).f0=IExec(T1,p,s6).f0 by Lm26,SCM_HALT:21;
  hence s.f0, IExec(bubble-sort f0,p,s).f0 are_fiberwise_equipotent
   by A2,A3,Lm33;
  let i,j be Nat;
  assume that
A5: i>=1 and
A6: j<=len (s.f0) and
A7: i<j;
  thus thesis by A2,A3,A4,A5,A6,A7,Lm33;
end;
