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Proof step 194 from proof refine-read-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, min(n1, n2) + n4 = n1 + n5, n3 + n5 + n1 = # buf3, LEB_SIZE = n0 + # buf0 + # buf, avol0[m2] = mapped(buf0 + buf), avol1[m2] = mapped(buf0 + buf), subarray(buf2, 0, n2) = subarray(buf, n3, n2), (n7 + min(n1, n2)) + n3 < # buf + n0, min(n1, n2) < n1 + n5, n3 < # buf3, n3 + n2 < # buf, n3 < # buf, m2 < # avol1, n2 < EB_PAGE_SIZE, # buf0 < LEB_SIZE, (n3 + # buf0) + n2 < LEB_SIZE, n3 < n0 + # buf, n7 < n4, min(n1, n2) + n7 < n1, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), min(n1, n2) ≤ EB_PAGE_SIZE, n1 + n3 ≤ # buf + n0 ⊦ (buf + mkempbuf(n0))[n3 + min(n1, n2) + n7] = ((n7 + min(n1, n2)) + n3 < # buf ⊃ buf[(n7 + min(n1, n2)) + n3];mkempbuf(n0)[(n7 + min(n1, n2)) + n3 - # buf])

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [n3 + min(n1, n2) + n7, mkempbuf(n0), buf] 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% ⊦ # mkempbuf(n) = n; (s)% ⊦ m + m0 < n + n0 → (m + m0 < n + n0 ↔ true); (ss)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s) Used terms: n3 + min(n1, n2) + n7, mkempbuf(n0), buf