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Proof step 90 from proof inv-format (previous step)

# buf1 = EB_PAGE_SIZE, # pebs1 = n + m1, # pebs0 = n + m1, pebs1[m1] = mkpeb(buf0, m2, false), 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)), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ n = 0, ∀ n. n < # subarray(pebs1[m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)], 0, m1 + 1) → ubi-io-peb-initial(subarray(pebs1[m1, mkpeb(copy(buf1, 0, emptypeb, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)], 0, m1 + 1)[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 91:
# 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])

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ # subarray(pebs, m, n) = n; (s)