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`

feat(frontends/lean): ML-like notation for match and recursive equations 2015-02-26 00:20:44 +00:00			`definition diag : bool → bool → bool → nat`
			`\| diag _ tt ff := 1`
			`\| diag ff _ tt := 2`
			`\| diag tt ff _ := 3`
			`\| 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`