lean2/tests/lean/tst11.lean

definition xor (x y : Bool) : Bool := (not x) = y
infixr 50 ⊕ : xor
print xor true false
eval xor true true
eval xor true false
variable a : Bool
print a ⊕ a ⊕ a
check @subst
theorem EM2 (a : Bool) : a \/ (not a) :=
   case (fun x : Bool, x \/ (not x)) trivial trivial a
check EM2
check EM2 a
feat(frontends/lean): use lowercase commands, replace 'endscope' and 'endnamespace' with 'end' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 20:05:08 +00:00			`definition xor (x y : Bool) : Bool := (not x) = y`
			`infixr 50 ⊕ : xor`
feat(frontends/lean/parser): combine Echo and Show commands into the 'print' command Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 19:03:35 +00:00			`print xor true false`
feat(frontends/lean): use lowercase commands, replace 'endscope' and 'endnamespace' with 'end' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 20:05:08 +00:00			`eval xor true true`
			`eval xor true false`
			`variable a : Bool`
feat(frontends/lean/parser): combine Echo and Show commands into the 'print' command Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 19:03:35 +00:00			`print a ⊕ a ⊕ a`
feat(*): change name conventions for Lean builtin libraries Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-06 03:10:21 +00:00			`check @subst`
feat(frontends/lean): use lowercase commands, replace 'endscope' and 'endnamespace' with 'end' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 20:05:08 +00:00			`theorem EM2 (a : Bool) : a \/ (not a) :=`
feat(*): change name conventions for Lean builtin libraries Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-06 03:10:21 +00:00			`case (fun x : Bool, x \/ (not x)) trivial trivial a`
feat(frontends/lean): use lowercase commands, replace 'endscope' and 'endnamespace' with 'end' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 20:05:08 +00:00			`check EM2`
			`check EM2 a`