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Proof step 70 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)), 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)).align↓, is-aligned(# buf0 + n, EB_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 71:
⊦ is-aligned(# buf, EB_PAGE_SIZE) → buf.align↓ = buf
Proof step 72:
# lpt = # avol, # buf0 + n0 = align↓(# buf0 + n, EB_PAGE_SIZE), avol[m1] = mapped(buf0), m1 < # avol, awbuf-inv(avol, buffered(m1)), is-aligned(#(buf0 + subarray(buf, 0, 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 ⊦ (buf0 + subarray(buf, 0, n)).align↓ = buf0 + subarray(buf, 0, n0), is-aligned(# buf0 + n, EB_PAGE_SIZE)

Rule argument

spec: awbuf-inv name: align-down-is-aligned seq: ⊦ is-aligned(# buf, EB_PAGE_SIZE) → buf.align↓ = buf subst: [buf] → [buf0 + subarray(buf, 0, n0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # subarray(buf, m, n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0 ⊦ n = align↓(n0, m) → is-aligned(n, m); (ss) Used terms: buf0 + subarray(buf, 0, n0)