Before revision:  On the basis of these types, {\AE}THEL further provides 72 ,623 validated derivations, presented in four equivalent formats: natural-deduction and sequent-style proofs, linear logic proofnets and the associated programs (lambda terms) for meaning composition.
After revision:  On the basis of these types, {\AE}THEL further provides 72 ,623 validated derivations, presented in four formats: natural-deduction and sequent-style proofs, linear logic proofnets and the associated programs (lambda terms) for meaning composition.