22 lines
488 B
Text
22 lines
488 B
Text
open nat bool inhabited
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definition diag : bool → bool → bool → nat,
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diag _ tt ff := 1,
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diag ff _ tt := 2,
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diag tt ff _ := 3,
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diag _ _ _ := default 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 = default nat :=
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rfl
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theorem diag4_2 : diag tt tt tt = default nat :=
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rfl
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