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Proof step 72 from proof inv-write (previous step)

LEB_SIZE = n0 + m, LEB_SIZE = n4 + m1 + n1, avols[v][m2] = mapped(buf0, m), n1 < n, m2 < # avols[v], n3 < LEB_SIZE, n3 < n4, ebm-cons(avols), is-aligned(m, EB_PAGE_SIZE), is-aligned(n1, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), range=(buf0, m, emptyleb, 0, n0), v ∈ avols, n1 + m1 ≤ LEB_SIZE, m ≤ m1, m ≤ LEB_SIZE, n2 + n1 ≤ # buf, m1 + n ≤ LEB_SIZE, n + n2 ≤ # buf, m1 ≤ LEB_SIZE, m1 + n1 ≤ LEB_SIZE, n4 ≤ LEB_SIZE, ⌊err0⌋ ⊦ (subarray(buf, n2, n1) + mkempbuf(n4))[n1 + n3] = empty, n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 73:
⊦ n < # buf + # buf0 → (buf + buf0)[n] = (n < # buf ⊃ buf[n];buf0[n - # buf])

Rule argument

spec: array-splice, inst: buffer name: append-at seq: ⊦ n < # buf + # buf0 → (buf + buf0)[n] = (n < # buf ⊃ buf[n];buf0[n - # buf]) subst: [n, buf0, buf] → [n1 + n3, mkempbuf(n4), subarray(buf, n2, n1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n - m = n; (s)% ⊦ m < n → mkempbuf(n)[m] = empty; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: n1 + n3, mkempbuf(n4), subarray(buf, n2, n1)