lean2/examples/ex3.lean

Definition xor (x y : Bool) : Bool := (not x) = y
Infixr 50 ⊕ : xor
Show xor true false
Eval xor true true
Eval xor true false
Variable a : Bool
Show a ⊕ a ⊕ a
Check Subst::explicit
Theorem EM2 (a : Bool) : a \/ (not a) :=
   Case (fun x : Bool, x \/ (not x)) Trivial Trivial a
Check EM2
Check EM2 a
Add parse_theorem and parse_definition Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-08-18 19:48:02 +00:00			`Definition xor (x y : Bool) : Bool := (not x) = y`
Allow notation to be associated with arbitrary expression (instead of only constants). Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-08-20 00:25:15 +00:00			`Infixr 50 ⊕ : xor`
Add parse_theorem and parse_definition Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-08-18 19:48:02 +00:00			`Show xor true false`
			`Eval xor true true`
			`Eval xor true false`
			`Variable a : Bool`
			`Show a ⊕ a ⊕ a`
Mark implicit arguments of builtin symbols Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-08-30 22:56:04 +00:00			`Check Subst::explicit`
Add parse_theorem and parse_definition Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-08-18 19:48:02 +00:00			`Theorem EM2 (a : Bool) : a \/ (not a) :=`
			`Case (fun x : Bool, x \/ (not x)) Trivial Trivial a`
			`Check EM2`
			`Check EM2 a`