1 + 2 : ℕ
open_tst.lean:4:8: error: unknown identifier 'add'
a + a : ℕ
a + a : ℕ
open_tst.lean:12:10: error: type mismatch at application
  a + 1
term
  1
has type
  num
but is expected to have type
  ℕ
a + a : ℕ
a + a : ℕ
a + 1 : ℕ
open_tst.lean:22:2: error: don't know how to synthesize placeholder

⊢ inhabited ℕ
open_tst.lean:22:2: error: failed to add declaration 'foo1' to environment, value has metavariables
  ?M_1
a + a : ℕ
open_tst.lean:29:8: error: unknown identifier 'add'
a + 1 : ℕ
open_tst.lean:32:2: error: don't know how to synthesize placeholder

⊢ inhabited ℕ
open_tst.lean:32:2: error: failed to add declaration 'foo2' to environment, value has metavariables
  ?M_1
open_tst.lean:41:10: error: invalid expression