lean2/tests/lean/simp30.lean

37 lines
1.2 KiB
Text
Raw Normal View History

variable vec : Nat → Type
variable concat {n m : Nat} (v : vec n) (w : vec m) : vec (n + m)
infixl 65 ; : concat
axiom concat_assoc {n1 n2 n3 : Nat} (v1 : vec n1) (v2 : vec n2) (v3 : vec n3) :
(v1 ; v2) ; v3 = cast (to_heq (congr2 vec (symm (Nat::add_assoc n1 n2 n3))))
(v1 ; (v2 ; v3))
variable empty : vec 0
axiom concat_empty {n : Nat} (v : vec n) :
v ; empty = cast (to_heq (congr2 vec (symm (Nat::add_zeror n))))
v
rewrite_set simple
add_rewrite Nat::add_assoc Nat::add_zeror eq_id : simple
add_rewrite concat_assoc concat_empty Nat::add_assoc Nat::add_zeror : simple
(*
local opts = options({"simplifier", "heq"}, true)
local t = parse_lean('∀ (n : Nat) (v : vec (n + 0)) (w : vec n), v = w ; empty')
print(t)
local t2, pr = simplify(t, "simple", opts)
print("====>")
print(t2)
get_environment():type_check(pr)
*)
print ""
(*
local opts = options({"simplifier", "heq"}, true)
local t = parse_lean('λ n : Nat, ∃ (v : vec (n + 0)) (w : vec n), v ≠ w ; empty')
print(t)
local t2, pr = simplify(t, "simple", opts)
print("====>")
print(t2)
get_environment():type_check(pr)
*)