21 lines
650 B
Text
21 lines
650 B
Text
definition set (A : Type) := A → Prop
|
||
definition mem {A : Type} (a : A) (s : set A) : Prop :=
|
||
s a
|
||
definition range (lower : nat) (upper : nat) : set nat :=
|
||
λ a, lower ≤ a ∧ a ≤ upper
|
||
infix ` ∈ ` := mem
|
||
|
||
local notation `[` L `, ` U `]` := range L U
|
||
|
||
variables s : set nat
|
||
variables p : nat → nat → Prop
|
||
|
||
|
||
-- check a ∈ s
|
||
set_option pp.binder_types true
|
||
check ∀ b c a ∈ s, a + b + c > 0
|
||
-- ∀ (b c a : ℕ), b ∈ s → c ∈ s → a ∈ s → a + b + c > 0 : Prop
|
||
check ∀ a < 5, p a (a+1)
|
||
-- ∀ (a : ℕ), a < 5 → p a (a + 1) : Prop
|
||
check ∀ a b ∈ [2, 3], p a b
|
||
-- ∀ (a b : ℕ), a ∈ [2, 3] → b ∈ [2, 3] → p a b
|