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Proof step 6 from proof aligndown-simp (previous step)

((m + n) % EB_PAGE_SIZE = 0 ⊃ m + n;(m + n) / EB_PAGE_SIZE * EB_PAGE_SIZE) < EB_PAGE_SIZE, m < EB_PAGE_SIZE, ((m + n) % EB_PAGE_SIZE = 0 ⊃ m + n;(m + n) / EB_PAGE_SIZE * EB_PAGE_SIZE) < m, ((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) + 1 < EB_PAGE_SIZE, EB_PAGE_SIZE ≤ n + m ⊦ n = 0

User applied rule case distinction

And obtained the following new goals

Proof step 7:
((m + n) % EB_PAGE_SIZE = 0 ⊃ m + n;(m + n) / EB_PAGE_SIZE * EB_PAGE_SIZE) + 1 < EB_PAGE_SIZE, ((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) < n + m, ((m + n) % EB_PAGE_SIZE = 0 ⊃ m + n;(m + n) / EB_PAGE_SIZE * EB_PAGE_SIZE) < m, m < EB_PAGE_SIZE, (m + n) / EB_PAGE_SIZE * EB_PAGE_SIZE < EB_PAGE_SIZE, EB_PAGE_SIZE ≤ n + m ⊦ (m + n) % EB_PAGE_SIZE = 0, n = 0

Rule argument

pos: left 1

Additional information

Used simplifier rules: ⊦ m < n → m % n = m; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ m < n → n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic