45 lines
865 B
Text
45 lines
865 B
Text
import num tactic
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using num
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variable a : num
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add_rewrite fact_zero fact_succ one_eq_succ_zero
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(*
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local t1 = parse_lean("num::add num::one (num::succ num::one)")
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print(t1)
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print("====>")
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local t2, pr = simplify(t1)
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print(t2)
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print(get_environment():type_check(pr))
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*)
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print ""
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(*
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local t1 = parse_lean("num::mul (num::succ (num::succ num::one)) (num::succ num::one)")
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print(t1)
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print("====>")
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local t2, pr = simplify(t1)
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print(t2)
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print(get_environment():type_check(pr))
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*)
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print ""
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theorem T1 : one * (succ one) = (succ one)
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:= by simp
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theorem T2 : a * (succ one) = a + a
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:= by simp
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theorem T3 : one = succ zero
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:= refl one -- one is not opaque
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set_option simplifier::unfold true
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definition two := succ one
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definition three := succ two
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definition four := succ three
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set_option pp::implicit true
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theorem test : fact four = four * three * two
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:= by simp
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