lean2/tests/lean/tactic13.lean

Import Int.
(* import("tactic.lua") *)
Variable f : Int -> Int -> Int

(*
refl_tac           = apply_tac("Refl")
congr_tac          = apply_tac("Congr")
symm_tac           = apply_tac("Symm")
trans_tac          = apply_tac("Trans")
unfold_homo_eq_tac = unfold_tac("eq")
auto = unfold_homo_eq_tac .. Repeat(OrElse(refl_tac, congr_tac, assumption_tac(), Then(symm_tac, assumption_tac(), now_tac())))
*)

Theorem T1 (a b c : Int) (H1 : a = b) (H2 : a = c) : (f (f a a) b) = (f (f b c) a).
   auto.
   done.

Theorem T2 (a b c : Int) (H1 : a = b) (H2 : a = c) : (f (f a c)) = (f (f b a)).
   auto.
   done.

print Environment 2.
chore(builtin): rename nat, int and real modules to Nat, Int and Real. Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-01 21:52:25 +00:00			`Import Int.`
feat(frontends/lean): use '(* ... )' instead of '(* ... **)' for script code blocks Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 18:32:47 +00:00			`(* import("tactic.lua") *)`
feat(frontends/lean/parser): apply type inference elaborator to fill remaining metavariables/holes (these are holes produced by tactics such as apply_tac) Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-07 21:09:39 +00:00			`Variable f : Int -> Int -> Int`

feat(frontends/lean): use '(* ... )' instead of '(* ... **)' for script code blocks Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 18:32:47 +00:00			`(*`
feat(frontends/lean/parser): apply type inference elaborator to fill remaining metavariables/holes (these are holes produced by tactics such as apply_tac) Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-07 21:09:39 +00:00			`refl_tac = apply_tac("Refl")`
			`congr_tac = apply_tac("Congr")`
			`symm_tac = apply_tac("Symm")`
			`trans_tac = apply_tac("Trans")`
			`unfold_homo_eq_tac = unfold_tac("eq")`
refactor(frontends/lean/parser): tactic macros, and tactic Lua bindings Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-26 23:54:53 +00:00			`auto = unfold_homo_eq_tac .. Repeat(OrElse(refl_tac, congr_tac, assumption_tac(), Then(symm_tac, assumption_tac(), now_tac())))`
feat(frontends/lean): use '(* ... )' instead of '(* ... **)' for script code blocks Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 18:32:47 +00:00			`*)`
feat(frontends/lean/parser): apply type inference elaborator to fill remaining metavariables/holes (these are holes produced by tactics such as apply_tac) Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-07 21:09:39 +00:00
			`Theorem T1 (a b c : Int) (H1 : a = b) (H2 : a = c) : (f (f a a) b) = (f (f b c) a).`
refactor(frontends/lean/parser): tactic macros, and tactic Lua bindings Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-26 23:54:53 +00:00			`auto.`
feat(frontends/lean/parser): apply type inference elaborator to fill remaining metavariables/holes (these are holes produced by tactics such as apply_tac) Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-07 21:09:39 +00:00			`done.`

			`Theorem T2 (a b c : Int) (H1 : a = b) (H2 : a = c) : (f (f a c)) = (f (f b a)).`
refactor(frontends/lean/parser): tactic macros, and tactic Lua bindings Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-26 23:54:53 +00:00			`auto.`
feat(frontends/lean/parser): apply type inference elaborator to fill remaining metavariables/holes (these are holes produced by tactics such as apply_tac) Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-07 21:09:39 +00:00			`done.`

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 Environment 2.`