[Agda] simple question
Andrew Harris
andrew.unit at gmail.com
Tue Oct 14 04:13:41 CEST 2014
Hello,
I'm trying to follow along in the very good paper "Dependent Types At
Work" written by Ana Bove and Peter Dybjer. I'm stuck at trying to prove
"eq-succ", which is one of the exercises in Section 4.4. The closest I can
make it is the following:
{- proof of eq-succ -}
eq-succ : {n m : Nat} → n == m → succ n == succ m
eq-succ (refl m) = natrec {(\k → (k + m) == (plus k m))} (refl m) (\i h →
((succ i) + m) == (plus (succ i) m)) m
But this does not typecheck, I get the error:
Set !=< (succ i + m) == plus (succ i) m of type Set₁
when checking that the expression (succ i + m) == plus (succ i) m
has type (succ i + m) == plus (succ i) m
I'm stuck -- I don't quite understand what I'm supposed to create an
element of Set_1 that has a signature of (succ i + m) == plus (succ i) m, (if
that's what I'm supposed to do). Any hints would be appreciated!
-andrew
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