-- FILE: nat+ps.mod

-- in nat+.mod
mod! NAT+ {
  [Zero NzNat < Nat]
  op 0 : -> Zero
  op s_ : Nat -> NzNat
  op _+_ : Nat Nat -> Nat
  
  vars M N : Nat
  eq    0  + N = N .
  eq (s M) + N = s(M + N) .
}

open (NAT+ + EQL)
op n : -> Nat .
eq n = 0 .
red (n + n) + n = 0 .
close

open (NAT+ + EQL)
op n : -> Nat .
eq n + 0 = n .
red (s n) + 0 = s n .
close

--> start of proof score for (N + 0 = N)
open (NAT+ + EQL)
--> induction base
red 0 + 0 = 0 .
--> induction hypothesis
op n : -> Nat .
eq n + 0 = n .
--> induction step
red (s n) + 0 = s n .
close
--> end