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Proof step 7 from proof aligndown-simp (previous step)

((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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
(m + n) / EB_PAGE_SIZE = 0, m < EB_PAGE_SIZE, EB_PAGE_SIZE ≤ n + m ⊦ (m + n) % EB_PAGE_SIZE = 0, n + m = 0, EB_PAGE_SIZE = 1, m = 0, n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1; (ws)% ⊦ m < n → n ≠ 0; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ 0 * n = 0; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ m * n + n0 < n ↔ m = 0 ∧ n0 < n; (ws)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m0 * m < m ↔ m0 = 0 ∧ m ≠ 0; (ws)