Do we always apply our input to the left most term in a lamda expression?
For instance, take the expressions:
$λP λQ. ∀x P(x)→Q(x)$ which we can rewrite as $[λP λQ[ ∀x P(x)→Q(x)]]$
$λP. λQ. ∀x P(x)→Q(x)$ which we can rewrite as $[λP [λQ[ ∀x P(x)→Q(x)]]]$
If we apply an input to each expression, would the input in both expressions replace P? But if that's the case, wouldn't that make the two expressions equivalent?