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Proof step 191 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 ⊦ subarray(buf + mkempbuf(n0), 0, n1 + n3)[(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

Proof step 192:
⊦ n + m ≤ # buf ∧ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]
Proof step 193:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n3 + n5 + n1 = # buf3, min(n1, n2) + n4 = n1 + n5, LEB_SIZE = n0 + # buf0 + # buf, avol1[m2] = mapped(buf0 + buf), avol0[m2] = mapped(buf0 + buf), subarray(buf2, 0, n2) = subarray(buf, n3, n2), min(n1, n2) + n7 < n1, n7 < n4, n3 < n0 + # buf, (n3 + # buf0) + n2 < LEB_SIZE, # buf0 < LEB_SIZE, n2 < EB_PAGE_SIZE, m2 < # avol1, n3 < # buf, n3 + n2 < # buf, n3 < # buf3, min(n1, n2) < n1 + n5, (n7 + min(n1, n2)) + n3 < # buf + n0, (n3 + min(n1, n2)) + n7 < n1 + n3, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(n3 + # buf0, EB_PAGE_SIZE), n1 + n3 ≤ # buf + n0, min(n1, n2) ≤ EB_PAGE_SIZE, (n1 + n3) + 0 ≤ #(buf + mkempbuf(n0)) ⊦ (buf + mkempbuf(n0))[0 + (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])

Rule argument

spec: array-copy, inst: buffer name: at-subarray seq: ⊦ n + m ≤ # buf ∧ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0] subst: [n0, n, m, buf] → [(n3 + min(n1, n2)) + n7, n1 + n3, 0, buf + mkempbuf(n0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # mkempbuf(n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m + n < m + n0 ↔ n < n0; (s) Used terms: (n3 + min(n1, n2)) + n7, n1 + n3, 0, buf + mkempbuf(n0)