About the explanation of the ⊸ ⊢ rule

[xieyuheng]

About the explanation of the ⊸ ⊢ rule

The ⊸ ⊢ rule can be simplified to say that if one transaction produces an A for free and another transaction produces nothing for B, then we can combine both transactions together with a third transaction that can produce a B from an A.

If "for free" and "nothing for" is used in the explanation,
isn't it is about the rule without context?

Assumptions	Conclusion	Rule
⊢ A		⊸ ⊢
B ⊢ Λ	A ⊸ B ⊢

Which is only a special case of the rule with context:

Assumptions	Conclusion	Rule
Γ ⊢ A, Δ		⊸ ⊢
Θ, B ⊢ Λ	Γ, Θ, A ⊸ B ⊢ Δ, Λ