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Proof step 13 from proof align-down-app-same (previous step)

n < ((# buf0 + # buf1) % EB_PAGE_SIZE = 0 ⊃ # buf0 + # buf1;(# buf0 + # buf1) / EB_PAGE_SIZE * EB_PAGE_SIZE), # buf0 % EB_PAGE_SIZE + # buf1 < EB_PAGE_SIZE ⊦ 0 = EB_PAGE_SIZE, n < align↓(# buf0, EB_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
align↓(# buf0, EB_PAGE_SIZE) < ((# buf0 + # buf1) % EB_PAGE_SIZE = 0 ⊃ # buf0 + # buf1;(# buf0 + # buf1) / EB_PAGE_SIZE * EB_PAGE_SIZE), n < ((# buf0 + # buf1) % EB_PAGE_SIZE = 0 ⊃ # buf0 + # buf1;(# buf0 + # buf1) / EB_PAGE_SIZE * EB_PAGE_SIZE), # buf0 % EB_PAGE_SIZE + # buf1 < EB_PAGE_SIZE, align↓(# buf0, EB_PAGE_SIZE) ≤ n ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ EB_PAGE_SIZE ≠ 0; (s)