43 lines
851 B
Text
43 lines
851 B
Text
inductive T (a:Type) where
|
||
| constuctor1: T a
|
||
| constuctor2: T a
|
||
|
||
instance : LE (T a) where
|
||
le := sorry
|
||
|
||
axiom L: Type
|
||
axiom L.pred (l1: L) (t: T α): Prop
|
||
|
||
axiom L.pred_le (l1: L) (t1 t2: T α):
|
||
t1 ≤ t2 → l1.pred t1 → l1.pred t2
|
||
grind_pattern L.pred_le => t1 ≤ t2, l1.pred t1
|
||
|
||
abbrev T' := T Unit
|
||
|
||
axiom l (t: T'): L
|
||
|
||
-- l keeps the same value when t gets bigger
|
||
axiom l_le (t1 t2: T'):
|
||
t1 ≤ t2 → l t1 = l t2
|
||
grind_pattern l_le => t1 ≤ t2, l t1
|
||
|
||
-- construction using l and L.pred
|
||
abbrev pred (t: T'): Prop :=
|
||
(l t).pred t
|
||
|
||
example: pred t1 → t1 ≤ t2 → pred t2 := by
|
||
grind
|
||
|
||
example: t1 ≤ t2 → pred t1 → pred t2 := by
|
||
grind
|
||
|
||
def is_mono (p: T' → Prop): Prop :=
|
||
∀ t1 t2,
|
||
p t1 → t1 ≤ t2 → p t2
|
||
|
||
example: is_mono pred := by
|
||
grind [is_mono]
|
||
|
||
example: is_mono pred := by
|
||
unfold is_mono
|
||
grind
|