[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 51 from proof inv-format (previous step)

# pebs = n0 + m1, # pebs0 = n0 + m1, pebs[m1] = mkpeb(buf, m0, false), m = m1, mtd-cons(pebs), mtd-cons(pebs0), ubi-io-initial(subarray(pebs, 0, m1)) ⊦ [if m < # pebs ∧ ¬ pebs[m].bad then {fail_or_success#(; ; err); if err = ESUCCESS then pebs[m] := mkpeb(emptypeb, 0, pebs[m].bad)} else abort] ( mtd-cons(pebs) → ⟪err0 := err; if err0 = ESUCCESS then ubi_io_write_echdr#(m1, aechdr((err1 = ESUCCESS ∧ aehdr.valid? ⊃ aehdr.ec + 1;0)), EB_PAGE_SIZE; pebs; err0); m1 := m1 + 1⟫ ( m1 ≤ # pebs0 ∧ # pebs0 = # pebs ∧ mtd-cons(pebs) ∧ (err0 = ESUCCESS → ubi-io-initial(subarray(pebs, 0, m1))) ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ # pebs0 < n0 + m1)), n0 = 0

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 52:
# pebs0 = n0 + m1, # pebs = n0 + m1, pebs[m1] = mkpeb(buf, m0, false), m = m1, mtd-cons(pebs0), mtd-cons(pebs), ubi-io-initial(subarray(pebs, 0, m1)) ⊦ [fail_or_success#(; ; err); if err = ESUCCESS then pebs[m] := mkpeb(emptypeb, 0, pebs[m].bad)] ( mtd-cons(pebs) → ⟪err0 := err; if err0 = ESUCCESS then ubi_io_write_echdr#(m1, aechdr((err1 = ESUCCESS ∧ aehdr.valid? ⊃ aehdr.ec + 1;0)), EB_PAGE_SIZE; pebs; err0); m1 := m1 + 1⟫ ( m1 ≤ # pebs0 ∧ # pebs0 = # pebs ∧ mtd-cons(pebs) ∧ (err0 = ESUCCESS → ubi-io-initial(subarray(pebs, 0, m1))) ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ # pebs0 < n0 + m1)), n0 = 0

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ m < m + n ↔ n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkpeb(buf, m, boolvar).bad ↔ boolvar; (s)