24 lines
514 B
Text
24 lines
514 B
Text
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open nat bool inhabited prod
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definition diag (a b c : bool) : nat :=
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match (a, b, c) with
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(_, tt, ff) := 1,
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(ff, _, tt) := 2,
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(tt, ff, _) := 3,
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(_, _, _) := 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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