b5122b6a7b
This change * moves `termination_by` and `decreasing_by` next to the function they apply to * simplify the syntax of `termination_by` * apply the `decreasing_by` goal to all goals at once, for better interactive use. See the section in `RELEASES.md` for more details and migration advise. This is a hard breaking change, requiring developers to touch every `termination_by` in their code base. We decided to still do it as a hard-breaking change, because supporting both old and new syntax at the same time would be non-trivial, and not save that much. Moreover, this requires changes to some metaprograms that developers might have written, and supporting both syntaxes at the same time would make _their_ migration harder.
37 lines
780 B
Text
37 lines
780 B
Text
mutual
|
|
@[simp] def isEven : Nat → Bool
|
|
| 0 => true
|
|
| n+1 => isOdd n
|
|
decreasing_by apply Nat.lt_succ_self
|
|
|
|
@[simp] def isOdd : Nat → Bool
|
|
| 0 => false
|
|
| n+1 => isEven n
|
|
decreasing_by apply Nat.lt_succ_self
|
|
end
|
|
|
|
theorem isEven_double (x : Nat) : isEven (2 * x) = true := by
|
|
induction x with
|
|
| zero => simp
|
|
| succ x ih => simp [Nat.mul_succ, Nat.add_succ, ih]
|
|
|
|
def f (x : Nat) : Nat :=
|
|
match x with
|
|
| 0 => 1
|
|
| x + 1 => f x * 2
|
|
decreasing_by apply Nat.lt_succ_self
|
|
|
|
attribute [simp] f
|
|
|
|
theorem f_succ (x : Nat) : f (x+1) = f x * 2 := by
|
|
simp
|
|
|
|
theorem f_succ₂ (x : Nat) : f (x+1) = f x * 2 := by
|
|
fail_if_success simp [-f]
|
|
simp
|
|
|
|
attribute [-simp] f
|
|
|
|
theorem f_succ₃ (x : Nat) : f (x+1) = f x * 2 := by
|
|
fail_if_success simp
|
|
simp [f]
|