quantities in case don't need to be *exactly* the same

...as long as they are all compatible with the target.
for example, given ω.n : ℕ:
```
  case double_it? return ℕ of {
    'true  ⇒ plus n n;
    'false ⇒ n
  }
```

lib/Quox/Syntax/Qty.idr

@@ -12,6 +12,7 @@ public export
 interface Eq q => IsQty q where
   zero, one : q
   (+),  (*) : q -> q -> q
+  lub       : q -> q -> Maybe q
 
   ||| true if bindings of this quantity will be erased
   ||| and must not be runtime relevant
@@ -19,9 +20,9 @@ interface Eq q => IsQty q where
   isZero : Dec1 IsZero
   zeroIsZero : IsZero zero
 
-  ||| ``p `Compat` q`` if it is ok for a binding of
-  ||| quantity `q` to be used exactly `p` times.
-  ||| e.g. ``1 `Compat` 1``, ``1 `Compat` ω``
+  ||| ``p `Compat` q`` if it is ok for a binding of quantity `q` to be used
+  ||| exactly `p` times. e.g. ``1 `Compat` 1``, ``1 `Compat` ω``.
+  ||| if ``π `lub` ρ`` exists, then both `π` and `ρ` must be compatible with it
   Compat : Rel q
   compat : Dec2 Compat
 

lib/Quox/Syntax/Qty/Three.idr

@@ -50,6 +50,13 @@ times One  rh   = rh
 times pi   One  = pi
 times Any  Any  = Any
 
+public export
+lub3 : Three -> Three -> Maybe Three
+lub3 p q =
+  if p == Any || q == Any then Just Any
+  else if p == q then Just p
+  else Nothing
+
 public export
 data Compat3 : Rel Three where
   CmpRefl : Compat3 rh rh
@@ -103,6 +110,8 @@ IsQty Three where
   (+) = plus
   (*) = times
 
+  lub = lub3
+
   IsZero     = Equal Zero
   isZero     = decEq Zero
   zeroIsZero = Refl