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Proof step 29 from proof inv-write (previous step)

LEB_SIZE = n3 + m1 + n, LEB_SIZE = n0 + m, avols[v][m2] = mapped(buf0, m), n1 < LEB_SIZE, n1 < n3, m2 < # avols[v], (m1 + n) + n1 < # subarray(buf0, 0, m1) + #(subarray(buf, n2, n) + mkempbuf(n3)), ebm-cons(avols), is-aligned(m, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), range=(buf0, m, emptyleb, 0, n0), v ∈ avols, n3 ≤ LEB_SIZE, m ≤ LEB_SIZE, m1 ≤ LEB_SIZE, n2 + n ≤ # buf, m1 + n ≤ LEB_SIZE, n + n2 ≤ # buf, m ≤ m1, n + m1 ≤ LEB_SIZE ⊦ ((m1 + n) + n1 < # subarray(buf0, 0, m1) ⊃ subarray(buf0, 0, m1)[(m1 + n) + n1] ;(subarray(buf, n2, n) + mkempbuf(n3))[(m1 + n) + n1 - # subarray(buf0, 0, m1)] ) = empty, n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
LEB_SIZE = n0 + m, LEB_SIZE = n3 + m1 + n, avols[v][m2] = mapped(buf0, m), m2 < # avols[v], n1 < LEB_SIZE, n1 < n3, ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(m, EB_PAGE_SIZE), range=(buf0, m, emptyleb, 0, n0), v ∈ avols, n + m1 ≤ LEB_SIZE, m ≤ m1, n + n2 ≤ # buf, m1 + n ≤ LEB_SIZE, n2 + n ≤ # buf, m1 ≤ LEB_SIZE, m ≤ LEB_SIZE, n3 ≤ LEB_SIZE ⊦ (subarray(buf, n2, n) + mkempbuf(n3))[n + n1] = empty, n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ m + n - m = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ # subarray(buf, m, n) = n; (s)