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I don't know if the summary I provided is what's really going on here, but I'm a little baffled why this doesn't typecheck. I can't see what injectivity has to do with it, since we're not trying to deduce that the arguments are the same from the result of an application being the same; rather we're doing the opposite. I've encountered plenty of obvious arithmetic laws that I've needed to unsafeCoerceConstraint away with doing type level arithmetic, but this seems like it should be trivial regardless.

{-# LANGUAGE GADTs, ExplicitNamespaces, TypeOperators, DataKinds #-}
{-# LANGUAGE ConstraintKinds, KindSignatures, PatternGuards #-}

import Data.Type.Equality ((:~:)(..))
import GHC.TypeLits (Nat, type (<=), type (-), type (+), type (<=?))

data SNat :: Nat -> * where
    SSucc   :: SNat a -> SNat (a + 1)
    SZero   :: SNat 0

heqHet :: SNat a -> SNat b -> Maybe (a :~: b)
heqHet SZero SZero = Just Refl
heqHet (SSucc a) (SSucc b)
    | Just Refl <- heqHet a b = Just Refl
heqHet _ _ = Nothing

data Slice :: Nat -> Nat -> * where
    Slice   :: ((start + 1) <= end, end <= numElements)
            => SNat numElements -> SNat start -> SNat end
            -> Slice numElements (end - start)

heqHet' :: Slice a b -> Slice a b' -> Bool
heqHet' (Slice _ start end) (Slice _ start' end')
    | Just _ <- heqHet start start'
    , Just _ <- heqHet end end' = True
    | otherwise = False

Slice.hs:24:10:
    Could not deduce (((start + 1) <=? a) ~ ((start + 1) <=? a))
    from the context (b ~ (end - start), (start + 1) <= end, end <= a)
      bound by a pattern with constructor
                 Slice :: forall (numElements :: Nat) (start :: Nat) (end :: Nat).
                          ((start + 1) <= end, end <= numElements) =>
                          SNat numElements
                          -> SNat start -> SNat end -> Slice numElements (end - start),
               in an equation for ‘heqHet'’
      at Slice.hs:24:10-26
    or from (b' ~ (end1 - start1), (start1 + 1) <= end1, end1 <= a)
      bound by a pattern with constructor
                 Slice :: forall (numElements :: Nat) (start :: Nat) (end :: Nat).
                          ((start + 1) <= end, end <= numElements) =>
                          SNat numElements
                          -> SNat start -> SNat end -> Slice numElements (end - start),
               in an equation for ‘heqHet'’
      at Slice.hs:24:30-48
    NB: ‘GHC.TypeLits.<=?’ is a type function, and may not be injective
    Relevant bindings include
      heqHet' :: Slice a b -> Slice a b' -> Bool (bound at Slice.hs:24:1)
    In the pattern: Slice _ start end
    In an equation for ‘heqHet'’:
        heqHet' (Slice _ start end) (Slice _ start' end')
          | Just _ <- heqHet start start', Just _ <- heqHet end end' = True
          | otherwise = False
Failed, modules loaded: none.

Trac metadata

Trac field	Value
Version	7.10.2
Type	Bug
TypeOfFailure	OtherFailure
Priority	normal
Resolution	Unresolved
Component	Compiler (Type checker)
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