[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 16 from proof refine-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, rofs ↔ rofs0, avol0[m4] = mapped(buf2), adr = adr0, avol = avol1, bleb = buffered(m4), lpt = lpt0, m0 = m3, n0 = n, ns = ns0, plog = plog0, rofs0, m2 < EB_PAGE_SIZE, m4 < # avol1, abs(avol1, buffered(m4), mkwbuf(buf1, m1, m2), avol0, true), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(m1, EB_PAGE_SIZE), n ≤ # buf, # avol1[m4].data + n ≤ LEB_SIZE, m1 ≤ # buf2 ⊦ ⟨if bleb ≠ nobuffer ∧ # avol[bleb.leb].data + n0 ≤ LEB_SIZE ∧ n0 ≤ # buf then if rofs then err := EROFS else {fail_or_success#(; ; err); let m = bleb.leb in if err = ESUCCESS then avol[m] := mapped(avol[m].data + subarray(buf, 0, n0)) else { choose n with n ≠ 0 ∧ n < n0 ∧ is-aligned(# avol[m].data + n, EB_PAGE_SIZE) in avol[m] := mapped(avol[m].data + subarray(buf, 0, n)) ifnone skip or skip; rofs := true}} else abort⟩ (abs(avol, buffered(m4), mkwbuf(buf1, m1, m2), avol0, true) ∧ rofs ∧ EROFS = err)

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 17:
# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, rofs ↔ rofs0, avol0[m4] = mapped(buf2), adr = adr0, avol = avol1, bleb = buffered(m4), lpt = lpt0, m0 = m3, n0 = n, ns = ns0, plog = plog0, rofs0, m4 < # avol1, m2 < EB_PAGE_SIZE, abs(avol1, buffered(m4), mkwbuf(buf1, m1, m2), avol0, true), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(m1, EB_PAGE_SIZE), m1 ≤ # buf2, # avol1[m4].data + n ≤ LEB_SIZE, n ≤ # buf ⊦ ⟨if rofs then err := EROFS else {fail_or_success#(; ; err); let m = bleb.leb in if err = ESUCCESS then avol[m] := mapped(avol[m].data + subarray(buf, 0, n0)) else { choose n with n ≠ 0 ∧ n < n0 ∧ is-aligned(# avol[m].data + n, EB_PAGE_SIZE) in avol[m] := mapped(avol[m].data + subarray(buf, 0, n)) ifnone skip or skip; rofs := true}}⟩ (abs(avol, buffered(m4), mkwbuf(buf1, m1, m2), avol0, true) ∧ rofs ∧ EROFS = err)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ buffered(m).leb = m; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # avol ⊦ abs(avol, bleb, wbuf, avol0, rofs) ∧ avol0[n] = mapped(buf) → (avol[n].mapped? ↔ true); (ss)% ⊦ buffered(m).isbuf?; (s)% ⊦ nobuffer ≠ buffered(m); (s)