local env = environment()
local A = Local("A", Type)
env = add_decl(env, mk_var_decl("eq", Pi(A, mk_arrow(A, A, Bool))))
local eq = Const("eq")
local a  = Local("a", A)
local b  = Local("b", A)
local H  = Local("H", eq(A, a, b))
local m  = mk_metavar("m", Pi(A, a, b, H, eq(A, a, b)))
print(to_proof_state(m))
local s  = to_proof_state(m)
local n, g = s:goals():head()
local hs   = g:hyps()
local h    = hs:head()
local pm   = proof_map()
pm:insert("main", h)
local r    = s:pb(pm, substitution())
print(r)
assert(env:infer_type(r) == env:infer_type(m))