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Proof step 73 from proof synced-write-buf (previous step)

# lpt = # avol, # buf0 + n0 = align↓(# buf0 + n, EB_PAGE_SIZE), avol[m1] = mapped(buf0), m1 < # avol, awbuf-inv(avol, buffered(m1)), is-aligned(# buf0 + n0, EB_PAGE_SIZE), avol0 ↓ avol[m1, mapped(buf0 + subarray(buf, 0, n))], n0 ≤ # buf, EB_PAGE_SIZE ≤ # buf0 % EB_PAGE_SIZE + n, # buf0 + n ≤ LEB_SIZE, n ≤ # buf ⊦ (buf0 + subarray(buf, 0, n)).align↓ = buf0 + subarray(buf, 0, n0), is-aligned(# buf0 + n, EB_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 74:
⊦ buf.align↓ = subarray(buf, 0, align↓(# buf, EB_PAGE_SIZE))
Proof step 75:
# lpt = # avol, # buf0 + n0 = align↓(# buf0 + n, EB_PAGE_SIZE), avol[m1] = mapped(buf0), m1 < # avol, awbuf-inv(avol, buffered(m1)), is-aligned(# buf0 + n0, EB_PAGE_SIZE), avol0 ↓ avol[m1, mapped(buf0 + subarray(buf, 0, n))], n ≤ # buf, # buf0 + n ≤ LEB_SIZE, EB_PAGE_SIZE ≤ # buf0 % EB_PAGE_SIZE + n, n0 ≤ # buf ⊦ subarray(buf0 + subarray(buf, 0, n), 0, align↓(#(buf0 + subarray(buf, 0, n)), EB_PAGE_SIZE)) = buf0 + subarray(buf, 0, n0), is-aligned(# buf0 + n, EB_PAGE_SIZE)

Rule argument

spec: awbuf-inv name: down-arrow-buf seq: ⊦ buf.align↓ = subarray(buf, 0, align↓(# buf, EB_PAGE_SIZE)) subst: [buf] → [buf0 + subarray(buf, 0, n)] flags: <all paths>

Additional information

Used terms: buf0 + subarray(buf, 0, n)