diff --git a/src/plfa/Induction.lagda b/src/plfa/Induction.lagda index c450df23..91389c36 100644 --- a/src/plfa/Induction.lagda +++ b/src/plfa/Induction.lagda @@ -497,9 +497,10 @@ time we are concerned with judgements asserting associativity. Now, we apply the rules to all the judgements we know about. The base case tells us that `(zero + n) + p ≡ zero + (n + p)` for every natural `n` and `p`. The inductive case tells us that if `(m + n) + p ≡ m + -(n + p)` (on the day before today) then `(suc m + n) + p ≡ suc m + (n -+ p)` (today). We didn't know any judgments about associativity -before today, so that rule doesn't give us any new judgments. +(n + p)` (on the day before today) then +`(suc m + n) + p ≡ suc m + (n + p)` (today). +We didn't know any judgments about associativity before today, so that +rule doesn't give us any new judgments. -- on the first day, we know about associativity of 0 (0 + 0) + 0 ≡ 0 + (0 + 0) ... (0 + 4) + 5 ≡ 0 + (4 + 5) ...