The base case

Defining a function

The assumption that the statement holds for a previous case

The conclusion of the proof

m + n

m + 1

succ (add m n)

m + zero = m

By repeated predecessor function

By repeated successor function

By repeated subtraction

By repeated addition

double

int

float

nat

ff

tt

error

Two subgoals are generated, one for z = tt and one for z = ff, but no reduction occurs.

change

trivial

dsimp

rewrite

cases x

dsimp

refl

equal

To analyze one possibility of x.

To prove x = tt.

To analyze the two possibilities of x.

To prove x = ff.

ff

tt

Depends on the context

error

RAA is not valid in classical logic.

RAA states that to prove P, it is sufficient to show that ¬P leads to a contradiction.

RAA is used to prove ¬P by assuming P.

RAA is the same as Double Negation Elimination.