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Proof step 3 from proof datasize-alignup (previous step)

is-aligned(n, EB_PAGE_SIZE), n ≤ # buf ⊦ datasize(buf, align↑(datasize(buf, n), EB_PAGE_SIZE)) = datasize(buf, n)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ n0 ≤ # buf ∧ n0 ≤ n1 → (datasize(buf, n0) = datasize(buf, n1) ↔ (∀ n. n0 ≤ n ∧ n < n1 → buf[n] = empty))
Proof step 5:
is-aligned(n, EB_PAGE_SIZE), n ≤ # buf ⊦ datasize(buf, align↑(datasize(buf, n), EB_PAGE_SIZE)) = datasize(buf, n), align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ # buf ∧ align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ n
Proof step 8:
is-aligned(n, EB_PAGE_SIZE), n ≤ # buf, align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ # buf, align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ n ⊦ ∀ n2. align↑(datasize(buf, n), EB_PAGE_SIZE) ≤ n2 ∧ n2 < n → buf[n2] = empty

Rule argument

spec: datasize name: datasize-further seq: ⊦ n0 ≤ # buf ∧ n0 ≤ n1 → ( datasize(buf, n0) = datasize(buf, n1) ↔ (∀ n. n0 ≤ n ∧ n < n1 → buf[n] = empty)) subst: [n1, n0, buf] → [n, align↑(datasize(buf, n), EB_PAGE_SIZE), buf] flags: <all paths>

Additional information

Used terms: n, align↑(datasize(buf, n), EB_PAGE_SIZE), buf