Solution
= Solution
From $\rho(x)=\sup_{y\in x}(\rho(y)+1)$, if every $\rho(y)<\gamma$, then every $\rho(y)+1\le\gamma$ and the supremum is at most $\gamma$, contradicting $\gamma<\rho(x)$.
= Solution
From $\rho(x)=\sup_{y\in x}(\rho(y)+1)$, if every $\rho(y)<\gamma$, then every $\rho(y)+1\le\gamma$ and the supremum is at most $\gamma$, contradicting $\gamma<\rho(x)$.