[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 91 from proof inv-format (previous step)

# pebs0 = n + m1, # pebs1 = n + m1, # buf1 = EB_PAGE_SIZE, pebs1[m1] = mkpeb(buf0, m2, false), is-encoded(echdr((err1 = ESUCCESS ∧ aehdr0.valid? ⊃ aehdr0.ec + 1;0)), buf1), mtd-cons(pebs0), mtd-cons(pebs1), mtd-cons(pebs1[m1, mkpeb(emptypeb, 0, false)]), mtd-cons(pebs1[m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)]), ubi-io-initial(subarray(pebs1, 0, m1)), EB_PAGE_SIZE ≤ PEB_SIZE, n0 ≤ m1 ⊦ n = 0, ubi-io-peb-initial(subarray(pebs1[m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)], 0, m1 + 1)[n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 92:
⊦ n + m ≤ # pebs ∧ n0 < n → subarray(pebs, m, n)[n0] = pebs[m + n0]
Proof step 93:
# buf1 = EB_PAGE_SIZE, # pebs1 = n + m1, # pebs0 = n + m1, pebs1[m1] = mkpeb(buf0, m2, false), n0 < m1 + 1, is-encoded(echdr((err1 = ESUCCESS ∧ aehdr0.valid? ⊃ aehdr0.ec + 1;0)), buf1), mtd-cons(pebs1[m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)]), mtd-cons(pebs1[m1, mkpeb(emptypeb, 0, false)]), mtd-cons(pebs1), mtd-cons(pebs0), ubi-io-initial(subarray(pebs1, 0, m1)), n0 ≤ m1, EB_PAGE_SIZE ≤ PEB_SIZE, (m1 + 1) + 0 ≤ # pebs1[m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)] ⊦ n = 0, ubi-io-peb-initial(pebs1[m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)][0 + n0])

Rule argument

spec: array-copy, inst: pebs name: at-subarray seq: ⊦ n + m ≤ # pebs ∧ n0 < n → subarray(pebs, m, n)[n0] = pebs[m + n0] subst: [n0, n, m, pebs] → [n0, m1 + 1, 0, pebs1 [m1, mkpeb (copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false) ]] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # pebs[n, peb] = # pebs; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s) Used terms: n0, m1 + 1, 0, pebs1 [m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false) ]