22 lines
478 B
Text
22 lines
478 B
Text
open nat bool inhabited
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definition diag : bool → bool → bool → nat
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| b tt ff := 1
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| ff b tt := 2
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| tt ff b := 3
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| b1 b2 b3 := arbitrary nat
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theorem diag1 (a : bool) : diag a tt ff = 1 :=
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bool.cases_on a rfl rfl
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theorem diag2 (a : bool) : diag ff a tt = 2 :=
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bool.cases_on a rfl rfl
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theorem diag3 (a : bool) : diag tt ff a = 3 :=
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bool.cases_on a rfl rfl
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theorem diag4_1 : diag ff ff ff = arbitrary nat :=
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rfl
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theorem diag4_2 : diag tt tt tt = arbitrary nat :=
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rfl
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