[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 28 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) = 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, n3 ≠ 0, 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), n0 ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE ⊦ ⟪apersistence_io_write# (buffered(m4).leb, # buf2, 0, n0 + m2, copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 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)

Rule argument

Additional information

Used simplifier rules: nat1: ⊦ n0 = n1 + n → (n0 ≤ n1 + m ↔ n ≤ m);% ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic