If a language has a converb with the fundamental meaning of succession, then it has also a converb with the fundamental meaning of precedence. The existence of the latter usually also presupposes the existence of a converb with the fundamental meaning of simultaneity.
Standardized
IF there are converbs with the fundamental meaning of succession, THEN there are converbs with the fundamental meaning of precedence. IF there are converbs with the fundamental meaning of precedence, THEN there are converbs with the fundamental meaning of simultaneity.
Converb is a verb form which depends syntactically on another verb form, but not its syntactic actant, i.e., does not realize its semantic valences. Thus a canonical (i.e. noncombined) converb can occupy (1) the position of an adjunct, i.e. an adverbial, but cannot occupy the positions: (2) of the only predicate of a simple sentence (without additional auxiliary elements); (3) of nominal attributes; (4) of a clausal actant (i.e. it cannot depend on verbs such as ‘begin’, ‘order’, etc.); (5) of a nominal actant (i.e. it does not occur in subject and object position) (Nedjalkov 1995: 97).
Converb is a verb form which depends syntactically on another verb form, but not its syntactic actant, i.e., does not realize its semantic valences. Thus a canonical (i.e. noncombined) converb can occupy (1) the position of an adjunct, i.e. an adverbial, but cannot occupy the positions: (2) of the only predicate of a simple sentence (without additional auxiliary elements); (3) of nominal attributes; (4) of a clausal actant (i.e. it cannot depend on verbs such as ‘begin’, ‘order’, etc.); (5) of a nominal actant (i.e. it does not occur in subject and object position) (Nedjalkov 1995: 97).