Help would be appreciated. The notes are poor on the subject, and I am clueless.
Verify the following equalities:
Verify the equality $$\mathsf{SIII}=_β\mathsf{I}$$ where $\mathsf{S} = λxyz.(xz)(yz) \quad \mathsf{I}= λx.x$
Verify the equality $$\operatorname{twice} (\operatorname{twice}) f x =_β f(f(f(f x)))$$ where $\operatorname{twice} = λfx.f(f x)$
Try substituting the arguments in the definitions of the combinators.