open nat definition foo : nat → nat | foo (0 + x) := x definition foo : nat → nat → nat | foo 0 _ := 0 | foo x ⌞y⌟ := x definition foo : nat → nat → nat | foo 0 _ := 0 | foo ⌞x⌟ x := x inductive tree (A : Type) := | node : tree_list A → tree A | leaf : A → tree A with tree_list := | nil {} : tree_list A | cons : tree A → tree_list A → tree_list A definition is_leaf {A : Type} : tree A → bool with is_leaf_aux : tree_list A → bool | is_leaf (tree.node _) := bool.ff | is_leaf (tree.leaf _) := bool.tt | is_leaf_aux tree_list.nil := bool.ff | is_leaf_aux (tree_list.cons _ _) := bool.ff definition foo : nat → nat | foo 0 := 0 | foo (x+1) := let y := x + 2 in y * y example : foo 5 = 36 := rfl definition boo : nat → nat | boo (x + 1) := boo (x + 2) | boo 0 := 0