This is really an Agda question, but because it involves HoTT concepts, and 
because there are several Agda formalizers here, I prefer to ask it here 
rather than in the Agda mailing list.

Forgive me is the question has a simple answer.

Consider the following constructions:

is-set' : ∀ {U} → U ̇ → U ̇
is-set' X = {x y : X} → is-prop(x ≡ y)

is-set' : ∀ {U} → U ̇ → U ̇
is-set' X = (x y : X) → is-prop(x ≡ y)

is-set'-is-set : ∀ {U} {X : U ̇} → is-set' X → is-set X
is-set'-is-set s {x} {y} = s x y

is-set-is-set' : ∀ {U} {X : U ̇} → is-set X → is-set' X
is-set-is-set' s x y = s {x} {y}

is-prop-is-set' : ∀ {U} {X : U ̇} → funext U U → is-prop (is-set' X)
is-prop-is-set' fe = is-prop-exponential-ideal fe
                               (λ x → is-prop-exponential-ideal fe
                               (λ y → is-prop-is-prop fe))

Now I am not able to prove that 

is-prop-is-set : ∀ {U} {X : U ̇} → funext U U → is-prop (is-set X)

The reason is that funext has explicit parameters, and I don't seem to be 
able to get funext with implicit parameters from funext with explicit 
parameters. Am I missing something obvious?

(I am tempted to make is-set' the official version and ditch is-set, but 
this will involve major rewriting of the Agda code.)

Martin

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