[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 9 from proof inv-read-vidhdr (previous step)

pebs[m0] = mkpeb(buf0, m1, false), buf = mkbuf(EB_PAGE_SIZE), m0 < # pebs, mtd-cons(pebs) ⊦ ⟪ubi_io_read#(m0, EB_PAGE_SIZE, 0, EB_PAGE_SIZE, pebs; buf; bitflips, err); if err = ESUCCESS then if buf = mkempbuf(# buf) then avhdr := empty else let vhdr = ? in {decode_vidheader#(EB_PAGE_SIZE, buf; vhdr; err); if err = ESUCCESS then avhdr := avidhdr(vhdr.vol, vhdr.leb, vhdr.sqn, vhdr.size, vhdr.checksum)}⟫ true

User applied rule insert program lemma

And obtained the following new goals

Proof step 10:
mtd-cons(pebs), m < # pebs, ¬ pebs[m].bad, m0 + n ≤ PEB_SIZE, n0 + n ≤ # buf, buf0 = buf ⊦ ⟪ubi_io_read#(m, m0, n0, n, pebs; buf; bitflips, err)⟫ ( # buf = # buf0 ∧ range=(buf, 0, buf0, 0, n0) ∧ range=(buf, n0 + n, buf0, n0 + n, # buf0 - n0 + n) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → subarray(buf, n0, n) = subarray(pebs[m].data, m0, n)))
Proof step 11:
pebs[m0] = mkpeb(buf0, m1, false), buf = mkbuf(EB_PAGE_SIZE), buf = buf, buf1 = buf, m2 = m0, m3 = EB_PAGE_SIZE, n1 = EB_PAGE_SIZE, n2 = 0, pebs0 = pebs, m0 < # pebs, mtd-cons(pebs), EB_PAGE_SIZE + EB_PAGE_SIZE ≤ PEB_SIZE, 0 + EB_PAGE_SIZE ≤ # buf ⊦ [ubi_io_read#(m0, EB_PAGE_SIZE, 0, EB_PAGE_SIZE, pebs; buf; bitflips, err)] ( # buf = # buf1 ∧ range=(buf, 0, buf1, 0, n2) ∧ range=(buf, n2 + n1, buf1, n2 + n1, # buf1 - n2 + n1) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → subarray(buf, n2, n1) = subarray(pebs0[m2].data, m3, n1)) → ⟪if err = ESUCCESS then if buf = mkempbuf(# buf) then avhdr := empty else let vhdr = ? in {decode_vidheader#(EB_PAGE_SIZE, buf; vhdr; err); if err = ESUCCESS then avhdr := avidhdr(vhdr.vol, vhdr.leb, vhdr.sqn, vhdr.size, vhdr.checksum)}⟫ true), pebs[m0].bad

Rule argument

spec: <toplevel> name: inv-io-read seq: mtd-cons(pebs), m < # pebs, ¬ pebs[m].bad, m0 + n ≤ PEB_SIZE, n0 + n ≤ # buf, buf0 = buf ⊦ ⟪ubi_io_read#(m, m0, n0, n, pebs; buf; bitflips, err)⟫ ( # buf = # buf0 ∧ range=(buf, 0, buf0, 0, n0) ∧ range=(buf, n0 + n, buf0, n0 + n, # buf0 - n0 + n) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → subarray(buf, n0, n) = subarray(pebs[m].data, m0, n))) subst: [pebs, n, n0, m0, m, buf, err, bitflips, buf0] → [pebs, EB_PAGE_SIZE, 0, EB_PAGE_SIZE, m0, buf, err, bitflips, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + m = 2 * m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ m ≤ m; (s)% ⊦ mkpeb(buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ PEB_SIZE < 2 * EB_PAGE_SIZE; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult