20c616503a
This PR implements a basic `grind?` tactic companion for `grind`. We will add more bells and whistles later.
81 lines
2.1 KiB
Text
81 lines
2.1 KiB
Text
attribute [grind =] List.length_cons
|
||
attribute [grind →] List.getElem?_eq_getElem
|
||
attribute [grind =] List.length_replicate
|
||
attribute [grind =] List.getElem_replicate
|
||
attribute [grind =] List.getElem?_eq_none
|
||
attribute [grind =] List.getElem?_eq_some_iff
|
||
attribute [grind =] getElem!_pos
|
||
|
||
attribute [grind =] Option.map_some' Option.map_none'
|
||
attribute [grind =] List.getElem?_map
|
||
attribute [grind =] List.getElem?_replicate
|
||
|
||
attribute [grind =] List.getLast?_eq_some_iff
|
||
attribute [grind] List.mem_concat_self
|
||
|
||
attribute [grind =] List.getElem_cons_zero in
|
||
attribute [grind =] List.getElem?_cons_zero in
|
||
|
||
/--
|
||
info: Try this: grind only [= List.getElem?_replicate, = List.getElem?_eq_none]
|
||
-/
|
||
#guard_msgs (info) in
|
||
theorem getElem?_replicate' : (List.replicate n a)[m]? = if m < n then some a else none := by
|
||
grind?
|
||
|
||
/--
|
||
info: Try this: grind only [= List.length_cons]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : 0 < (x :: t).length := by
|
||
grind?
|
||
|
||
/--
|
||
info: Try this: grind only [= List.getElem?_replicate, = List.getElem?_eq_some_iff, = List.getElem?_map, =
|
||
List.getElem_replicate, = List.getElem?_eq_none, = Option.map_some', = Option.map_none', = List.length_replicate, →
|
||
List.getElem?_eq_getElem, cases And, cases Or, cases Exists]
|
||
-/
|
||
#guard_msgs (info) in
|
||
theorem map_replicate' : (List.replicate n a).map f = List.replicate n (f a) := by
|
||
grind?
|
||
|
||
/--
|
||
info: Try this: grind only [= List.getLast?_eq_some_iff, List.mem_concat_self, cases Exists]
|
||
-/
|
||
#guard_msgs (info) in
|
||
theorem mem_of_getLast?_eq_some' {xs : List α} {a : α} (h : xs.getLast? = some a) : a ∈ xs := by
|
||
grind?
|
||
|
||
def f : Nat → Nat
|
||
| 0 => 1
|
||
| _ => 2
|
||
|
||
/--
|
||
info: Try this: grind only
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : x = 0 → f x = 1 := by
|
||
unfold f
|
||
grind? -- should not include match equations
|
||
|
||
attribute [grind] f
|
||
|
||
/--
|
||
info: Try this: grind only [f]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : x = 0 → f x = 1 := by
|
||
grind? [f]
|
||
|
||
opaque g : Nat → Nat
|
||
|
||
theorem gthm : g (g x) = g x := sorry
|
||
|
||
grind_pattern gthm => g (g x)
|
||
|
||
/--
|
||
info: Try this: grind only [usr gthm]
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : g (g (g x)) = g x := by
|
||
grind?
|