DEFINITION minus_plus_r()
TYPE =
∀m:nat.∀n:nat.(eq nat (minus (plus m n) n) m)
BODY =
assume m: nat
assume n: nat
(h1)
by (minus_plus . .)
eq nat (minus (plus n m) n) m
end of h1
(h2)
by (plus_sym . .)
eq nat (plus m n) (plus n m)
end of h2
by (eq_ind_r . . . h1 . h2)
we proved eq nat (minus (plus m n) n) m
we proved ∀m:nat.∀n:nat.(eq nat (minus (plus m n) n) m)