42 lines
1.4 KiB
Text
42 lines
1.4 KiB
Text
def fact : Nat → Nat
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| 0 => 1
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| (n+1) => (n+1)*fact n
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#eval fact 10
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#eval fact 100
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new_frontend
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theorem tst1 : fact 10 = 3628800 :=
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nativeRefl! (fact 10)
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theorem tst2 : fact 100 = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 :=
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nativeRefl! (fact 100)
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theorem tst3 : decide (10000000000000000 < 200000000000000000000) = true :=
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nativeRefl! (decide (10000000000000000 < 200000000000000000000))
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theorem tst4 : 10000000000000000 < 200000000000000000000 :=
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ofDecideEqTrue (nativeRefl! (decide (10000000000000000 < 200000000000000000000)))
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theorem tst5 : 10000000000000000 < 200000000000000000000 :=
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nativeDecide! (10000000000000000 < 200000000000000000000)
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theorem tst6 : 10000000000000000 < 200000000000000000000 :=
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let h₁ := nativeDecide! (10000000000000000 < 10000000000000010);
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let h₂ := nativeDecide! (10000000000000010 < 200000000000000000000);
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Nat.ltTrans h₁ h₂
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theorem tst7 : 10000000000000000 < 200000000000000000000 :=
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decide! (10000000000000000 < 200000000000000000000)
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theorem tst8 : 10000000000000000 < 200000000000000000000 :=
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let h₁ := decide! (10000000000000000 < 10000000000000010);
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let h₂ := decide! (10000000000000010 < 200000000000000000000);
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Nat.ltTrans h₁ h₂
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theorem tst9 : 10000000000000000 < 200000000000000000000 :=
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decide! _
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theorem tst10 : 10000000000000000 < 200000000000000000000 :=
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nativeDecide! _
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