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| P ⊢ Q | |
| ----- →-Intro | |
| P → Q | |
| P → Q P | |
| -------------- →-Elim | |
| Q | |
| ----------- name_encoder | |
| Name → JSON | |
| ---------- age_encoder | |
| Age → JSON | |
| ---------------------------------------------- employee_encoder | |
| (Name → JSON) → (Age → JSON) → Employee → JSON | |
| ------------------------------------- department_encoder | |
| (Employee → JSON) → Department → JSON | |
| ------------------------------------ company_encoder | |
| (Department → JSON) → Company → JSON | |
| ------- company | |
| Company | |
| ---------------------------------------------- employee_encoder ----------- name_encoder | |
| (Name → JSON) → (Age → JSON) → Employee → JSON Name → JSON | |
| ---------------------------------------------------------------------------------- →-Elim ---------- age_encoder | |
| (Age → JSON) → Employee → JSON Age → JSON | |
| ------------------------------------- department_encoder ----------------------------------------------------------------------------------------------------------- →-Elim | |
| (Employee → JSON) → Department → JSON Employee → JSON | |
| ------------------------------------ company_encoder ------------------------------------------------------------------------------- →-Elim | |
| (Department → JSON) → Company → JSON Department → JSON | |
| ----------------------------------------------------------------------------- →-Elim ------- company | |
| Company → JSON Company | |
| --------------------------------------------------------------------------------------------------- →-Elim | |
| JSON |
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