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Proof step 84 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf + n5 + n1 = # buf3, LEB_SIZE = n3 + n2 + # buf0 + # buf, avol1[m2] = mapped((buf0 + buf) + subarray(buf2, 0, n2)), avol0[m2] = mapped(buf0 + buf), n1 + 1 < EB_PAGE_SIZE, n1 < n2, m2 < # avol1, n2 < EB_PAGE_SIZE, n1 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf0 + # buf, EB_PAGE_SIZE), n1 ≤ n2 + n3, # buf0 ≤ LEB_SIZE, # buf ≤ # buf3 ⊦ subarray(buf2, 0, n1) = subarray(subarray(buf2, 0, n2), 0, n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 85:
n2 ≤ n1 ⊦ n1 < # buf → subarray(subarray(buf, 0, n1), 0, n2) = subarray(buf, 0, n2)

Rule argument

spec: array-copy, inst: buffer name: subarray-subarray-elim-0 seq: n2 ≤ n1 ⊦ n1 < # buf → subarray(subarray(buf, 0, n1), 0, n2) = subarray(buf, 0, n2) subst: [n2, n1, buf] → [n1, n2, buf2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ n < n; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: n1, n2, buf2