reserve s for State of SCM+FSA,
  I for MacroInstruction of SCM+FSA,
  a for read-write Int-Location;
reserve i,j,k,n for Nat;
reserve P,P1,P2,Q for Instruction-Sequence of SCM+FSA;

theorem Th22:
  for f being FinSeq-Location holds card insert-sort f = 71
proof
  set m1=Macro SubFrom(a2,a2), m2=AddTo(a4,a0), m3=SubFrom(a2,a0), IF=if>0(a5,
  m1, m2 ";" m3);
  let f be FinSeq-Location;
  set i1= a2:=a3, i2= SubFrom(a3,a0), i3= a5:=(f,a2), i4= a6:=(f,a3), i5= (f,
  a2):=a6, i6= (f,a3):=a5, body3= i1 ";" i2 ";" i3 ";" i4 ";" i5 ";" i6;
A1: card IF = card m1 + card (m2 ";" m3)+ 4 by SCMFSA8B:12
    .= 2 + card (m2 ";" m3)+ 4 by COMPOS_1:56
    .= 2 + (2 + 2)+ 4 by SCMFSA6A:35
    .= 10;
  set n1=a5:=(f,a2), n2=SubFrom(a5,a6), body2=n1 ";"n2 ";" IF;
A2: card body2 = card (n1 ";"n2) + card IF by SCMFSA6A:21
    .= 2 + 2 + 10 by A1,SCMFSA6A:35
    .= 14;
  set WM=initializeWorkMem, j1=a1:=len f, j2=SubFrom(a1,a0);
  set T3=Times(a4,body3), t1=a2:=len f, t2=SubFrom(a2,a1), t3=a3 := a2, t4=
  AddTo(a3,a0), t5=a6:=(f,a3), t6=SubFrom(a4,a4), Wg=while>0(a2,body2), t16=t1
  ";" t2 ";" t3 ";" t4 ";" t5 ";" t6, body1=t16 ";" Wg ";" T3;
A3: card body3 =
     card (i1 ";" i2 ";" i3 ";" i4 ";" i5) + 2 by SCMFSA6A:34
     .= 10+2 by Th21
    .=12;
A4: card body1 = card (t16 ";" Wg) + card T3 by SCMFSA6A:21
    .= card t16 + card Wg + card T3 by SCMFSA6A:21
    .= card (t1 ";" t2 ";" t3 ";" t4 ";" t5) + 2 + card Wg +
  card T3 by SCMFSA6A:34
    .= 10 + 2 + card Wg + card T3 by Th21
    .= 10 + 2 + (14 + 5) + card T3 by A2,SCMFSA_X:4
    .= 10 + 2 + (14 + 5) + (12+7) by A3,SCMFSA8C:94
    .= 50;
  thus card (insert-sort f) = card (WM ";" j1 ";" j2 ) + card Times(a1,body1)
  by SCMFSA6A:21
    .= card (WM ";" j1 ";" j2 ) + (50+7) by A4,SCMFSA8C:94
    .= card (WM ";" j1) + 2 + (50+7) by SCMFSA6A:34
    .= card WM + 2 + 2 + (50+7) by SCMFSA6A:34
    .= 10 + 2 + 2 + 57 by Th21
    .= 71;
end;
