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

# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, n1 + m2 ≠ 0, n3 ≠ 0, m2 < EB_PAGE_SIZE, m4 < # avol1, n1 < n0, n1 < # buf3, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(n1 + m2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(# buf2, EB_PAGE_SIZE), # avol1[m4].data + n3 ≤ LEB_SIZE, n3 ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, # buf2 + m2 + n3 ≤ LEB_SIZE, n0 ≤ # buf3, # buf2 + n0 + m2 ≤ LEB_SIZE, ⌊err1⌋ ⊦ n1 ≠ 0 ∧ n1 < n3 ∧ is-aligned(# avol1[m4].data + n1, EB_PAGE_SIZE) ∧ ⟨avol1[buffered(m4).leb] := mapped(avol1[buffered(m4).leb].data + subarray(buf3, 0, n1)); rofs := true⟩ ( abs (avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0[m4, mapped(avol0[m4].data + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2))], true) ∧ rofs)

Heuristic dl case distinction applied rule case distinction

And obtained the following new goals

Proof step 133:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, n1 < # buf3, n1 < n0, m4 < # avol1, m2 < EB_PAGE_SIZE, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(n1 + m2, EB_PAGE_SIZE), # buf2 + n0 + m2 ≤ LEB_SIZE, n0 ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, ⌊err1⌋ ⊦ n1 + m2 = 0, n3 = 0, is-aligned(# avol1[m4].data + n1, EB_PAGE_SIZE)
Proof step 139:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, n1 < # buf3, n1 < n0, m4 < # avol1, m2 < EB_PAGE_SIZE, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(n1 + m2, EB_PAGE_SIZE), # buf2 + n0 + m2 ≤ LEB_SIZE, n0 ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, ⌊err1⌋ ⊦ ⟨avol1[buffered(m4).leb] := mapped(avol1[buffered(m4).leb].data + subarray(buf3, 0, n1)); rofs := true⟩ ( abs (avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0[m4, mapped(avol0[m4].data + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2))], true) ∧ rofs), n1 + m2 = 0, n3 = 0

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0 ⊦ align↓(n0 + n1, m) = n2 + n1 → ¬ n0 < n2; (s)% ⊦ n + 0 = n; (s)%n ≠ 0 ⊦ is-aligned(n0, n) → align↓(n0 + n1, n) = n0 + align↓(n1, n); (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%m ≠ 0 ⊦ is-aligned(n, m) → (n < m ↔ n = 0); (s)