4848ad4869
Right now, it only supports the following kind of definitions - Recursive definitions that support smart unfolding. - Non-recursive definitions where the body is a match-expression. This kind of definition is only unfolded if the match can be reduced.
37 lines
984 B
Text
37 lines
984 B
Text
def append (as bs : List α) : List α :=
|
||
match as with
|
||
| [] => bs
|
||
| a :: as => a :: append as bs
|
||
|
||
theorem append_nil (as : List α) : append as [] = as := by
|
||
induction as <;> simp_all!
|
||
|
||
theorem append_nil' (as : List α) : append as [] = as := by
|
||
induction as <;> simp! [*]
|
||
|
||
theorem append_assoc (as bs cs : List α) : append (append as bs) cs = append as (append bs cs) := by
|
||
induction as <;> simp_all!
|
||
|
||
theorem append_assoc' (as bs cs : List α) : append (append as bs) cs = append as (append bs cs) := by
|
||
induction as <;> simp! [*]
|
||
|
||
def g : Nat → Nat
|
||
| 0 => 1
|
||
| n+1 => n + 2
|
||
|
||
example (a : Nat) : g a > 0 := by
|
||
cases a <;> simp_arith!
|
||
|
||
example (a : Nat) : g a > 0 := by
|
||
cases a <;> simp_arith!
|
||
|
||
example (a : Nat) : g a > 0 := by
|
||
cases a <;> simp_arith! [-g]
|
||
simp_arith!
|
||
|
||
example (a : Nat) (h : b + 2 = 2) : g a > b := by
|
||
cases a <;> simp_all_arith!
|
||
|
||
example (a : Nat) (h : b + 2 = 2) : g a > b := by
|
||
cases a <;> simp_all_arith! [-g]
|
||
simp_arith!
|