lean2/tests/lean/run/eq12.lean

open nat bool inhabited

definition diag : bool → bool → bool → nat,
diag _  tt ff := 1,
diag ff _  tt := 2,
diag tt ff _  := 3,
diag _  _  _  := arbitrary nat

theorem diag1 (a : bool) : diag a tt ff = 1 :=
bool.cases_on a rfl rfl

theorem diag2 (a : bool) : diag ff a tt = 2 :=
bool.cases_on a rfl rfl

theorem diag3 (a : bool) : diag tt ff a = 3 :=
bool.cases_on a rfl rfl

theorem diag4_1 : diag ff ff ff = arbitrary nat :=
rfl

theorem diag4_2 : diag tt tt tt = arbitrary nat :=
rfl
test(tests/lean/run): add more overlapping patterns examples 2015-01-05 20:25:14 +00:00			`open nat bool inhabited`

			`definition diag : bool → bool → bool → nat,`
			`diag _ tt ff := 1,`
			`diag ff _ tt := 2,`
			`diag tt ff _ := 3,`
feat(library/init/logic): add 'arbitrary' It is identical to default, but it is opaque. That is, when we use 'arbitrary A', we cannot rely on the particular value selected. 2015-01-05 21:27:09 +00:00			`diag _ _ _ := arbitrary nat`
test(tests/lean/run): add more overlapping patterns examples 2015-01-05 20:25:14 +00:00
			`theorem diag1 (a : bool) : diag a tt ff = 1 :=`
			`bool.cases_on a rfl rfl`

			`theorem diag2 (a : bool) : diag ff a tt = 2 :=`
			`bool.cases_on a rfl rfl`

			`theorem diag3 (a : bool) : diag tt ff a = 3 :=`
			`bool.cases_on a rfl rfl`

feat(library/init/logic): add 'arbitrary' It is identical to default, but it is opaque. That is, when we use 'arbitrary A', we cannot rely on the particular value selected. 2015-01-05 21:27:09 +00:00			`theorem diag4_1 : diag ff ff ff = arbitrary nat :=`
test(tests/lean/run): add more overlapping patterns examples 2015-01-05 20:25:14 +00:00			`rfl`

feat(library/init/logic): add 'arbitrary' It is identical to default, but it is opaque. That is, when we use 'arbitrary A', we cannot rely on the particular value selected. 2015-01-05 21:27:09 +00:00			`theorem diag4_2 : diag tt tt tt = arbitrary nat :=`
test(tests/lean/run): add more overlapping patterns examples 2015-01-05 20:25:14 +00:00			`rfl`