User interface:Julian/sandbox



kind (nat) kind (formula)

var (nat x y z)

term (formula (= nat nat))

stmt (eqreflexive  (x = x)) # 1st Peano axiom stmt (eqsymmetric ((x = y)) (y = x)) # 2nd Peano axiom stmt (eqtransitive ((x = y) (y = z)) (x = z)) # 3rd Peano axiom

term (nat (0)) # 5th Peano axiom term (nat (succ nat)) # 6th Peano axiom, a

stmt (succfunc ((x = y)) ((succ x) = (succ y))) # 6th Peano axiom, b stmt (succinj  (((succ x) = (succ y))) (x = y)) # 8th Peano axiom

def ((1) (succ (0))) def ((2) (succ (1))) def ((3) (succ (2))) def ((4) (succ (3)))

term (nat (+ nat nat))

stmt (addsym  ((x + y) = (y + x))) stmt (addzero  (x = (x + (0)))) stmt (addsucc  ((succ (x + y)) = (x + (succ y))))

