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Proof step 11 from proof align-down-app-same (previous step)

# buf0 % EB_PAGE_SIZE + # buf1 < EB_PAGE_SIZE, n < align↓(# buf0 + # buf1, EB_PAGE_SIZE) ⊦ n < align↓(# buf0, EB_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
0 ≠ m ⊦ align↓(n, m) = (n % m = 0 ⊃ n;n / m * m)
Proof step 13:
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)

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, # buf0 + # buf1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s) Used terms: EB_PAGE_SIZE, # buf0 + # buf1