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Proof step 9 from proof dist-c (previous step)

⊦ n0 = dist(n, n0 + n), n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ m ≤ n → dist(m, n) = n - m

Rule argument

spec: <toplevel> name: dist-fst seq: ⊦ m ≤ n → dist(m, n) = n - m subst: [n, m] → [n0 + n, n] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + n - m = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ m + n < m; (s) Used terms: n0 + n, n