# Standardisation Theorem versus Leftmost reduction Theorem

According to Chris Hankin in his book (Lambda Calculus a Guide for Computer Scientists). A reduction sequence $$\sigma: M_0 \to^{\Delta_0} M_1 \to^{\Delta_1}M_2 \to^{\Delta_2}\ldots$$ is a standard reduction if for any pair $$(\Delta_i, \Delta_{i+1})$$, $$\Delta_{i+1}$$ is not a residual of a redex to left of $$\Delta_{i}$$ relative to the given reduction from $$M_{i}$$ to $$M_{i}$$. The Standardization Theorem says that if a term $$A$$ $$\beta$$-reduces to $$B$$, then there is a standard path from $$A$$ to $$B$$. On the other hand, in the leftmost strategy, outermost redex is always reduced first. The Leftmost Reduction Theorem says that if a term $$A$$ $$\beta$$-reduces to $$B$$, and $$B$$ is in $$\beta$$-normal form, then the leftmost strategy reaches $$B$$. My question is:

1- I'm not seeing the difference between the reductions Standardization and Leftmost, for me, it seems to say the same thing.

2- Why the Leftmost Reduction Theorem is a particular case of the standardization Theorem?