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Proof step 1 from proof dist-add-01 (conclusion)

⊦ dist(m + n, m0 + n) = dist(m, m0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ m ≤ n → dist(m, n) = n - m
Proof step 3:
⊦ dist(m + n, m0 + n) = dist(m, m0), m + n ≤ m0 + n
Proof step 8:
m + n ≤ m0 + n ⊦ m0 + n - m + n = dist(m, m0)

Rule argument

spec: <toplevel> name: dist-fst seq: ⊦ m ≤ n → dist(m, n) = n - m subst: [n, m] → [m0 + n, m + n] flags: <all paths>

Additional information

Used terms: m0 + n, m + n