### Working forward

This proof uses variables `x`

, `y`

, and `z`

, with a function `f`

.
Your mission this time is to combine the two function calls into
a single expression.

As before, the fact to be proved has two assumptions: `y = f x`

and `z = f y`

. Forward proofs start from the assumptions and focus
on transforming the conclusion into the conclusion of the goal.

It can be convenient to have all of the planned assumptions available throughout the proof, so the initial step has the planned assumptions as the initial conclusion, makeing it a true statement.

The variable `y`

is assumed equal to `f x`

, so we can replace its
occurrence in the conclusion. Then the `y = f x`

is no longer needed
in the conclusion, and it can be replaced by `T`

because it is
assumed. Prooftoys makes it convenient to use assumptions of the
current step in these ways.

#### ➭ **Back to the main track**

**Back to the main track**