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Proof step 27 from proof refine-write-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), n3 ≠ 0, m4 < # avol1, m2 < EB_PAGE_SIZE, 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), # buf2 + m2 + n3 ≤ LEB_SIZE, align↓(m2 + n3, EB_PAGE_SIZE) ≤ # buf3 + m2, # avol1[m4].data + n3 ≤ LEB_SIZE, n3 ≤ # buf3, m2 ≤ align↓(m2 + n3, EB_PAGE_SIZE), EB_PAGE_SIZE ≤ m2 + n3 ⊦ ⟪apersistence_io_write# (buffered(m4).leb, # buf2, 0, align↓(m2 + n3, EB_PAGE_SIZE), copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2), adr0, m3, plog0, lpt0, ns0 ; avol0 ; err); wbuf := mkwbuf(buf1, # buf2, m2); rofs := false; if err = ESUCCESS then {wbuf.content := copy(buf3, align↓(m2 + n3, EB_PAGE_SIZE) - m2, wbuf.content, 0, (m2 + n3) % EB_PAGE_SIZE); wbuf.offset := wbuf.offset + align↓(m2 + n3, EB_PAGE_SIZE); wbuf.nbytes := (m2 + n3) % EB_PAGE_SIZE} else rofs := true⟫ ⟨rofs0 := false; awbuf_write_buf#(n3, buf3, adr0, m3, plog0, lpt0, ns0, buffered(m4); avol1, rofs0; err0)⟩ (abs(avol1, buffered(m4), wbuf, avol0, rofs) ∧ (rofs0 ↔ rofs) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, 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), EB_PAGE_SIZE ≤ m2 + n3, m2 ≤ align↓(m2 + n3, EB_PAGE_SIZE), n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, align↓(m2 + n3, EB_PAGE_SIZE) ≤ # buf3 + m2, # buf2 + m2 + n3 ≤ LEB_SIZE ⊦ ⟪apersistence_io_write# (buffered(m4).leb, # buf2, 0, align↓(m2 + n3, EB_PAGE_SIZE), copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, n0), adr0, m3, plog0, lpt0, ns0 ; avol0 ; err); wbuf := mkwbuf(buf1, # buf2, m2); rofs := false; if err = ESUCCESS then {wbuf.content := copy(buf3, n0, wbuf.content, 0, (m2 + n3) % EB_PAGE_SIZE); wbuf.offset := wbuf.offset + align↓(m2 + n3, EB_PAGE_SIZE); wbuf.nbytes := (m2 + n3) % EB_PAGE_SIZE} else rofs := true⟫ ⟨rofs0 := false; awbuf_write_buf#(n3, buf3, adr0, m3, plog0, lpt0, ns0, buffered(m4); avol1, rofs0; err0)⟩ (abs(avol1, buffered(m4), wbuf, avol0, rofs) ∧ (rofs0 ↔ rofs) ∧ err = err0), n3 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m2, align↓(m2 + n3, EB_PAGE_SIZE), n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m2, align↓(m2 + n3, EB_PAGE_SIZE), n