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Proof step 82 from proof refine-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, n3 < n + (m2 + n3) % EB_PAGE_SIZE, # buf3 < n + (m2 + n3) % EB_PAGE_SIZE, m2 < EB_PAGE_SIZE, m4 < # avol1, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n + m2, EB_PAGE_SIZE), # buf2 + n + m2 ≤ LEB_SIZE, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, n ≤ # buf3 ⊦ (m2 + n3) % EB_PAGE_SIZE = 0, n + m2 = 0, n3 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 83:
⊦ m ≠ 0 → n % m = n - align↓(n, m)
Proof step 84:
# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, m4 < # avol1, m2 < EB_PAGE_SIZE, # buf3 < n + (m2 + n3 - align↓(m2 + n3, EB_PAGE_SIZE)), n3 < n + (m2 + n3 - align↓(m2 + n3, EB_PAGE_SIZE)), abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(n + m2, EB_PAGE_SIZE), is-aligned(# buf2, EB_PAGE_SIZE), n ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, n3 ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, # buf2 + m2 + n3 ≤ LEB_SIZE, # buf2 + n + m2 ≤ LEB_SIZE ⊦ n + m2 = 0, m2 + n3 - align↓(m2 + n3, EB_PAGE_SIZE) = 0, EB_PAGE_SIZE = 0, n3 = 0

Rule argument

spec: <toplevel> name: mod-to-aligndown-minus seq: ⊦ m ≠ 0 → n % m = n - align↓(n, m) subst: [m, n] → [EB_PAGE_SIZE, m2 + n3] flags: <all paths>

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s) Used terms: EB_PAGE_SIZE, m2 + n3