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Proof step 33 from proof valid-peb-write-valid-peb (previous step)

#(subarray(buf, 0, m0) + mkempbuf(n1)) = LEB_SIZE, LEB_SIZE = n1 + m0, LEB_SIZE = n0 + m, apebs[n] = mkpeb(aehdr, avidhdr(v, m2, m4, m3, checksum(subarray(buf, 0, m0) + mkempbuf(n1), m3)), subarray(buf, 0, m0) + mkempbuf(n1), m, false), subarray(subarray(buf, 0, m0) + mkempbuf(n1), m, n0) = mkempbuf(n0), aehdr.valid?, n < # apebs, is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ m0, m3 ≤ datasize(subarray(buf, 0, m0) + mkempbuf(n1)), m3 ≤ LEB_SIZE ⊦ aehdr = empty, m3 = 0, m3 ≤ (datasize(buf1) = 0 ⊃ datasize(subarray(buf, 0, m0) + mkempbuf(n1), m0);m0 + datasize(buf1)) ∧ checksum(subarray(buf, 0, m0) + mkempbuf(n1), m3) = checksum(subarray(subarray(buf, 0, m0) + mkempbuf(n1), 0, m0) + buf1, m3)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
LEB_SIZE = n1 + m0, LEB_SIZE = n0 + m, apebs[n] = mkpeb(aehdr, avidhdr(v, m2, m4, m3, checksum(subarray(buf, 0, m0), m3)), subarray(buf, 0, m0) + mkempbuf(n1), m, false), subarray(subarray(buf, 0, m0) + mkempbuf(n1), m, n0) = mkempbuf(n0), aehdr.valid?, n < # apebs, is-aligned(m, EB_PAGE_SIZE), m3 ≤ datasize(subarray(buf, 0, m0)), m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ m0, m3 ≤ m0, m3 ≤ LEB_SIZE ⊦ aehdr = empty, m3 = 0, m3 ≤ (datasize(buf1) = 0 ⊃ datasize(subarray(buf, 0, m0) + mkempbuf(n1), m0);m0 + datasize(buf1)) ∧ checksum(subarray(buf, 0, m0) + mkempbuf(n1), m3) = checksum(subarray(buf, 0, m0) + buf1, m3)

Rule argument

Additional information

Used simplifier rules: let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ n ≤ # buf0 → checksum(buf0 + buf1, n) = checksum(buf0, n); (s)%datasize-le-fwd: ⊦ m ≤ datasize(buf) → m ≤ # buf; (forward) from specification datasize%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)% ⊦ datasize(buf + mkempbuf(n)) = datasize(buf); (s)%c: ⊦ m + n = n + m; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)