[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 81 from proof refine-write (previous step)

# apebs0 = # wlar, LEB_SIZE = (n0 + n) + vtblpnum5, apebs0[n2] = mkpeb(aehdr, avhdr, buf2, m0, false), vols[v][vtblpnum3] = ⌜n2⌝ , avols[v][vtblpnum3] = mapped(buf2, m), wlar[n2] = wl-entry(m1, used), n ≠ 0, vtblpnum4 ≠ n2, aehdr.valid?, avhdr.valid?, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], n2 < # wlar, abs(avols, apebs0, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(vtblpnum5, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)]), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs0), unique-sqns(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)]), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-ebatbl (apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], wlar, vols, vtblpnum4), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum4), valid-wl(apebs0, wlar), valid-wl(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, false)], wlar), v ∈ vols, v ∈ avols, m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, vtblpnum5 + n ≤ LEB_SIZE, n + n3 ≤ # buf, m ≤ vtblpnum5, m0 ≤ vtblpnum5, vtblpnum5 ≤ LEB_SIZE, n + vtblpnum5 ≤ LEB_SIZE, n3 + n ≤ # buf, ¬ VTBL_VOLID ∈ vols ⊦ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n3, n, buf; avols; err1)⟩ ( abs (avols, apebs0 [vols[v][vtblpnum3].pnum, mkpeb (apebs0[vols[v][vtblpnum3].pnum].echdr, apebs0[vols[v][vtblpnum3].pnum].vidhdr, subarray(apebs0[vols[v][vtblpnum3].pnum].data, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n0), vtblpnum5 + n, apebs0[vols[v][vtblpnum3].pnum].bad) ], vols, q) ∧ ESUCCESS = err1)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 82:
# apebs0 = # wlar, LEB_SIZE = (n4 + n) + vtblpnum5, wlar[n2] = wl-entry(m1, used), avols[v][vtblpnum3] = mapped(buf2, m), vols[v][vtblpnum3] = ⌜n2⌝ , apebs0[n2] = mkpeb(aehdr, avhdr, buf2, m0, false), n0 = n, n1 = n3, vtblpnum = vtblpnum5, vtblpnum0 = vtblpnum3, avhdr.valid?, aehdr.valid?, n2 < # wlar, vtblpnum3 < # avols[v], vtblpnum3 < # vols[v], abs(avols, apebs0, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(vtblpnum5, EB_PAGE_SIZE), ubi-io-inv(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n4), vtblpnum5 + n, false)]), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n4), vtblpnum5 + n, false)]), unique-sqns(apebs0), valid-ebatbl (apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n4), vtblpnum5 + n, false)], wlar, vols, vtblpnum4), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-eraseq(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n4), vtblpnum5 + n, false)], q), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n4), vtblpnum5 + n, false)], sqnum), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum4), valid-wl(apebs0[n2, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n4), vtblpnum5 + n, false)], wlar), valid-wl(apebs0, wlar), v ∈ avols, v ∈ vols, n3 + n ≤ # buf, n + vtblpnum5 ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, m0 ≤ vtblpnum5, m ≤ vtblpnum5, n + n3 ≤ # buf, vtblpnum5 + n ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE ⊦ ⟨if v ∈ avols ∧ vtblpnum0 < # avols[v] ∧ vtblpnum + n0 ≤ LEB_SIZE ∧ is-aligned(vtblpnum, EB_PAGE_SIZE) ∧ is-aligned(n0, EB_PAGE_SIZE) ∧ n0 + n1 ≤ # buf ∧ (avols[v][vtblpnum0].mapped? → vtblpnum ≥ avols[v][vtblpnum0].fill) then {fail_or_success#(; ; err); if err = ESUCCESS then if avols[v][vtblpnum0].mapped? then if n0 ≠ 0 then avols[v][vtblpnum0] := mapped (subarray(avols[v][vtblpnum0].data, 0, vtblpnum) + subarray(buf, n1, n0) + mkempbuf(LEB_SIZE - vtblpnum - n0), vtblpnum + n0) else avols[v][vtblpnum0] := mapped(mkempbuf(vtblpnum) + subarray(buf, n1, n0) + mkempbuf(LEB_SIZE - vtblpnum - n0), vtblpnum + n0) else if avols[v][vtblpnum0].mapped? then choose n with n < n0 ∧ is-aligned(n, EB_PAGE_SIZE) in if n ≠ 0 then avols[v][vtblpnum0] := mapped (subarray(avols[v][vtblpnum0].data, 0, vtblpnum) + subarray(buf, n1, n) + mkempbuf(LEB_SIZE - vtblpnum - n), vtblpnum + n) ifnone skip else if n0 ≠ 0 then avols[v][vtblpnum0] := unmapped} else abort⟩ ( abs (avols, apebs0 [vols[v][vtblpnum3].pnum, mkpeb (apebs0[vols[v][vtblpnum3].pnum].echdr, apebs0[vols[v][vtblpnum3].pnum].vidhdr, subarray(apebs0[vols[v][vtblpnum3].pnum].data, 0, vtblpnum5) + subarray(buf, n3, n) + mkempbuf(n4), vtblpnum5 + n, apebs0[vols[v][vtblpnum3].pnum].bad) ], vols, q) ∧ ESUCCESS = err), n = 0, vtblpnum4 = n2, VTBL_VOLID ∈ vols

Rule argument

pos: right 1

Additional information

Used simplifier rules: ebm_write#(VOLID, LNUM, OFFSET, N0, N, BUF; AVOLS; ERR) {if VOLID ∈ AVOLS ∧ LNUM < # AVOLS[VOLID] ∧ OFFSET + N ≤ LEB_SIZE ∧ is-aligned(OFFSET, EB_PAGE_SIZE) ∧ is-aligned(N, EB_PAGE_SIZE) ∧ N + N0 ≤ # BUF ∧ (AVOLS[VOLID][LNUM].mapped? → OFFSET ≥ AVOLS[VOLID][LNUM].fill) then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then if AVOLS[VOLID][LNUM].mapped? then if N ≠ 0 then AVOLS[VOLID][LNUM] := mapped ( subarray (AVOLS[VOLID][LNUM].data, 0, OFFSET) + subarray(BUF, N0, N) + mkempbuf(LEB_SIZE - OFFSET - N), OFFSET + N) else AVOLS[VOLID][LNUM] := mapped ( mkempbuf(OFFSET) + subarray(BUF, N0, N) + mkempbuf(LEB_SIZE - OFFSET - N), OFFSET + N) else if AVOLS[VOLID][LNUM].mapped? then choose N1 with N1 < N ∧ is-aligned(N1, EB_PAGE_SIZE) in if N1 ≠ 0 then AVOLS[VOLID][LNUM] := mapped ( subarray (AVOLS[VOLID][LNUM].data, 0, OFFSET) + subarray(BUF, N0, N1) + mkempbuf(LEB_SIZE - OFFSET - N1), OFFSET + N1) ifnone skip else if N ≠ 0 then AVOLS[VOLID][LNUM] := unmapped} else abort };