Idris2-boot/tests/idris2/basic014/Rewrite.idr
Edwin Brady e9a3167e2f Even more tests
Small change needed to fix one - assume given implicits which are of the
form x@_ arise from types. It's a bit of a hack but I don't think
there's any need for anything more complicated.
2019-06-27 20:19:00 +01:00

20 lines
618 B
Idris

plusnZ : (n : Nat) -> n + 0 = n
plusnZ 0 = Refl
plusnZ (S k) = rewrite plusnZ k in Refl
plusnSm : (n, m : Nat) -> n + (S m) = S (n + m)
plusnSm Z m = Refl
plusnSm (S k) m = rewrite plusnSm k m in Refl
plusCommutes : (n, m : Nat) -> n + m = m + n
plusCommutes Z m = sym (plusnZ m)
plusCommutes (S k) m = rewrite plusCommutes k m in sym (plusnSm m k)
wrongCommutes : (n, m : Nat) -> n + m = m + n
wrongCommutes Z m = sym (plusnZ m)
wrongCommutes (S k) m = rewrite plusCommutes m k in ?bar
wrongCommutes2 : (n, m : Nat) -> n + m = m + n
wrongCommutes2 Z m = sym (plusnZ m)
wrongCommutes2 (S k) m = rewrite m in ?bar