29 lines
836 B
Lua
29 lines
836 B
Lua
import("util.lua")
|
|
local env = get_environment()
|
|
parse_lean_cmds([[
|
|
axiom Ax1 {A : TypeU} (P Q : A -> Bool) : (forall x : A, P x /\ Q x) = ((forall x : A, P x) /\ (forall x : A, Q x))
|
|
variable f : Nat -> Nat -> Nat
|
|
variable p : Nat -> Bool
|
|
]], env)
|
|
local Ax1 = env:find_object("Ax1"):get_type()
|
|
function body(e)
|
|
while (e:is_pi()) do
|
|
local _, _, r = e:fields()
|
|
e = r
|
|
end
|
|
return e
|
|
end
|
|
local p = body(Ax1):arg(2)
|
|
local t = parse_lean([[
|
|
forall x : Nat, p (f x 0) /\ f (f x x) 1 >= 0
|
|
]], env)
|
|
r = hop_match(p, t)
|
|
assert(r)
|
|
assert(#r == 3)
|
|
local p, f, x, Nat = Consts("p, f, x, Nat")
|
|
assert(r[1] == Nat)
|
|
assert(r[2] == fun(x, Nat, p(f(x, nVal(0)))))
|
|
assert(r[3] == fun(x, Nat, Const({"Nat", "ge"})(f(f(x, x), nVal(1)), nVal(0))))
|
|
for i = 1, #r do
|
|
print("#" .. tostring(i) .. " <--- " .. tostring(r[i]))
|
|
end
|