print(`Let A, B be forward and M be backward shift`):
print(`operators on a, b and m respectively.`):

print(`Denote the identity on the right-hand-side of Thm 1' by R`):

print(`Then we verify that R(a,b,m) satisfies the recurrence`):
print(``):

print((X(m-1,a,b)*X(m-1,a+1,b+1)-X(m-1,a+1,b)*X(m-1,a,b+1))/X(m,a,b)/X(m-2,a+1,b+1)=1,`or`):

print(M(R)*MAB(R)/R/MMAB(R)-AM(R)*BM(R)/R/MMAB(R)=1):
print(`Note that:`):

h:=n->(1-q^n):w:=n->(1+q^n):

Print(`Therefore,`):
b1:=w(m+a+b)*h(2*a-b+2*m)*h(2*b-a+2*m)*h(a+b+m):
bb3:=h(3*a+2*m)*h(3*b+2*m)*h(2*m):
b3:=expand(bb3):
print(M(R)/R/ABM(MR/R),`=`,b1/bb3):
print(`and`):
b2:=q^(2*m)*w(a+b+2*m)*h(2*a-b)*h(2*b-a)*h(a+b):
print(MA(R)/R/BM(MA(R)/R),`=`,b2/bb3):
print(`Finally,`):

print(M(R)/R/ABM(MR/R)-MA(R)/R/BM(MA(R)/R),`=`,simplify((b1-b2)/b3)):