Fix break verbatim
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1 changed files with 4 additions and 3 deletions
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@ -497,9 +497,10 @@ time we are concerned with judgements asserting associativity.
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Now, we apply the rules to all the judgements we know about. The base
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Now, we apply the rules to all the judgements we know about. The base
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case tells us that `(zero + n) + p ≡ zero + (n + p)` for every natural
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case tells us that `(zero + n) + p ≡ zero + (n + p)` for every natural
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`n` and `p`. The inductive case tells us that if `(m + n) + p ≡ m +
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`n` and `p`. The inductive case tells us that if `(m + n) + p ≡ m +
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(n + p)` (on the day before today) then `(suc m + n) + p ≡ suc m + (n
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(n + p)` (on the day before today) then
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+ p)` (today). We didn't know any judgments about associativity
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`(suc m + n) + p ≡ suc m + (n + p)` (today).
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before today, so that rule doesn't give us any new judgments.
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We didn't know any judgments about associativity before today, so that
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rule doesn't give us any new judgments.
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-- on the first day, we know about associativity of 0
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-- on the first day, we know about associativity of 0
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(0 + 0) + 0 ≡ 0 + (0 + 0) ... (0 + 4) + 5 ≡ 0 + (4 + 5) ...
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(0 + 0) + 0 ≡ 0 + (0 + 0) ... (0 + 4) + 5 ≡ 0 + (4 + 5) ...
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