[Agda] what is happening here?

[Thorsten Altenkirch]

I define

record isMonoid {A : Set}(e : A)(_•_ : A → A → A) : Prp where
  field
    lneutr : {x : A} → e • x ≡ x
    rneutr : {x : A} → x • e ≡ x
    assoc : {x y z : A} → (x • y) • z ≡ x • (y • z)

and I have shown all 3 properties, in particular:

assoc+ : {l m n : ℕ} → (l + m) + n ≡ l + (m + n)

but when I try

isMonoid : isMonoid zero _+_
+isMonoid = record {
  lneutr = lneutr+ ;
  rneutr = rneutr+ ;
  assoc = assoc+ }

I get some unsolved constraints, even though my proof and the goal are alpha-equivalent! Ok I can fix this by eta expanding:

  assoc = λ {x}{y}{z} → assoc+ {x}{y}{z}

But this shouldn’t be necessary.






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