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Proof step 132 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, # buf3 = n4 + n2, n1 + n5 = n4 + n2, (n0 + # buf4) + n3 + n2 = LEB_SIZE, avol1[m2] = mapped(buf4 + subarray(buf2, 0, n2 + n0)), avol0[m2] = mapped(buf4), n < n1, n < n4 + n2, n < n2 + n4, n0 < EB_PAGE_SIZE, n2 + n0 < EB_PAGE_SIZE, m2 < # avol1, n < n2, n < n2 + n3, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf4, EB_PAGE_SIZE), n2 ≤ n1, # buf4 ≤ LEB_SIZE, n1 ≤ n2 + n3 ⊦ EB_PAGE_SIZE = 1, buf2[n0 + n] = subarray(buf2, 0, n2 + n0)[n0 + n], n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [n0 + n, n2 + n0, 0, buf2] 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 = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]% ⊦ m < n → n ≠ 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: n0 + n, n2 + n0, 0, buf2