Theorem: TMA produces a male-optimal pairing
- Suppose, for a contradiction, that some boy gets rejected by his optimal girl during TMA. Let t be the earliest time at which this happened.
- In particular, at time t, some boy b got rejected by his optimal girl g because she said “maybe” to a preferred b*. By the definition of t, b* had not yet been rejected by his optimal girl.
- Therefore, b* likes g at least as much as his optimal.