theorem Threcursive05: :: POSET_2:26

for X, Y being non empty set
for D being Subset of X
for I1, I2 being Function of X,Y
for J1, J2 being Function of [:X,Y,Y:],Y
for E1, E2 being Function of X,X st E1,E2 is_well_founded_with_minimal_set D holds
ex f, g being Function of X,Y st
for x being Element of X holds
( ( x in D implies ( f . x = I1 . x & g . x = I2 . x ) ) & ( not x in D implies ( f . x = J1 . [x,(f . (E1 . x)),(g . (E2 . x))] & g . x = J2 . [x,(f . (E1 . x)),(g . (E2 . x))] ) ) )