Section Reflection.
Variables φ' ψ0' ψ1' : valuation.
Variable Hψ0' : substitute ψ0' (substitute φ' s') = substitute φ' t0'.
Variable Hψ1' : substitute ψ1' (substitute φ' s') = substitute φ' t1'.
End Reflection.
End RU2SemiU_LU2SemiU.
End Argument.

(* many-one reduction from right-uniform two-inequality semi-unification to left-uniform two-inequality semi-unification *)
Theorem reduction : RU2SemiU ⪯ LU2SemiU.