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Proof step 3 from proof aligndown-simp (previous step)

align↓(m + n, EB_PAGE_SIZE) < m, m < EB_PAGE_SIZE, align↓(m + n, EB_PAGE_SIZE) + 1 < EB_PAGE_SIZE, align↓(m + n, EB_PAGE_SIZE) < EB_PAGE_SIZE, align↓(m + n, EB_PAGE_SIZE) + 1 < n + m, align↓(m + n, EB_PAGE_SIZE) < n + m, EB_PAGE_SIZE ≤ n + m ⊦ n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
0 ≠ m ⊦ align↓(n, m) = (n % m = 0 ⊃ n;n / m * m)
Proof step 5:
((m + n) % EB_PAGE_SIZE = 0 ⊃ m + n;(m + n) / EB_PAGE_SIZE * EB_PAGE_SIZE) < n + m, ((m + n) % EB_PAGE_SIZE = 0 ⊃ m + n;(m + n) / EB_PAGE_SIZE * EB_PAGE_SIZE) + 1 < n + m, ((m + n) % EB_PAGE_SIZE = 0 ⊃ m + n;(m + n) / EB_PAGE_SIZE * EB_PAGE_SIZE) < EB_PAGE_SIZE, ((m + n) % EB_PAGE_SIZE = 0 ⊃ m + n;(m + n) / EB_PAGE_SIZE * EB_PAGE_SIZE) + 1 < EB_PAGE_SIZE, m < EB_PAGE_SIZE, ((m + n) % EB_PAGE_SIZE = 0 ⊃ m + n;(m + n) / EB_PAGE_SIZE * EB_PAGE_SIZE) < m, EB_PAGE_SIZE ≤ n + m ⊦ 0 = EB_PAGE_SIZE, n = 0

Rule argument

spec: align name: aligndown-def seq: 0 ≠ m ⊦ align↓(n, m) = (n % m = 0 ⊃ n;n / m * m) subst: [m, n] → [EB_PAGE_SIZE, m + n] flags: <all paths>

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s) Used terms: EB_PAGE_SIZE, m + n