[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 4 from proof crash-neutral-write (previous step)

# lpt = # avol, avol[m3] = mapped(buf0), adr = adr0, m = m2, m1 = m3, n0 = n, n1 = n2, ns = ns0, plog = plog0, m3 < # avol, ebm-vol-inv(avol), is-aligned(m0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), # buf0 ≤ m0, m0 + n ≤ LEB_SIZE, n2 + n ≤ # buf, avol ⊆ avol0 ⊦ ⟨if m1 < # avol ∧ avol[m1].mapped? ∧ # avol[m1].data ≤ m0 ∧ is-aligned(m0, EB_PAGE_SIZE) ∧ is-aligned(n0, EB_PAGE_SIZE) ∧ m0 + n0 ≤ LEB_SIZE ∧ n1 + n0 ≤ # buf then {fail_or_success#(; ; err); if err = ESUCCESS then if n0 ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n0)) else choose n with n < n0 ∧ is-aligned(n, EB_PAGE_SIZE) in if n ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n)) ifnone skip} else abort⟩ (avol ⊆ avol0)

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 5:
# lpt = # avol, avol[m3] = mapped(buf0), adr = adr0, m = m2, m1 = m3, n0 = n, n1 = n2, ns = ns0, plog = plog0, m3 < # avol, ebm-vol-inv(avol), is-aligned(n, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), n2 + n ≤ # buf, m0 + n ≤ LEB_SIZE, # buf0 ≤ m0, avol ⊆ avol0 ⊦ ⟨fail_or_success#(; ; err); if err = ESUCCESS then if n0 ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n0)) else choose n with n < n0 ∧ is-aligned(n, EB_PAGE_SIZE) in if n ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n)) ifnone skip⟩ (avol ⊆ avol0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)