27 lines
1.1 KiB
Text
27 lines
1.1 KiB
Text
import tactic
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variable list : Type → Type
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variable nil {A : Type} : list A
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variable cons {A : Type} : A → list A → list A
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variable map {A B : Type} : (A → B) → list A → list B
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axiom map_cons {A B : Type} (f : A → B) (a : A) (l : list A) : map f (cons a l) = cons (f a) (map f l)
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axiom map_nil {A B : Type} (f : A → B) : (map f nil) = nil
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add_rewrite map_cons map_nil
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(*
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local m = simplifier_monitor(function(s, e)
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print("Visit, depth: " .. s:depth() .. ", " .. tostring(e))
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end,
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function(s, e, new_e, pr)
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print("Step: " .. tostring(e) .. " ===> " .. tostring(new_e))
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end,
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function(s, e, new_e, ceq, ceq_id)
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print("Rewrite using: " .. tostring(ceq_id))
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print(" " .. tostring(e) .. " ===> " .. tostring(new_e))
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end
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)
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set_simplifier_monitor(m)
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*)
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theorem T1 : map (λ x, x + 1) (cons 1 (cons 2 nil)) = cons 2 (cons 3 nil)
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:= by simp
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