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