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Proof step 45 from proof refine-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, rofs ↔ false, rofs0 ↔ false, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, err = err0, err = ESUCCESS, wbuf = mkwbuf(buf1, # buf2, m2), buffered(m4).isbuf?, avol0[buffered(m4).leb].mapped?, m4 < # avol1, m2 < EB_PAGE_SIZE, buffered(m4).leb < # avol0, 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(n + m2, EB_PAGE_SIZE), # buf2 + n + m2 ≤ LEB_SIZE, n ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, 0 + m2 ≤ # mkbuf(n + m2), 0 + m2 ≤ # buf1, m2 + n ≤ # copy(buf1, 0, mkbuf(n + m2), 0, m2), 0 + n ≤ # buf3, 0 + n + m2 ≤ # copy(buf3, 0, copy(buf1, 0, mkbuf(n + m2), 0, m2), m2, n), 0 + (m2 + n3) % EB_PAGE_SIZE ≤ # wbuf.content, n + (m2 + n3) % EB_PAGE_SIZE ≤ # buf3, # buf2 ≥ # avol0[buffered(m4).leb].data, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨awbuf_write_buf#(n3, buf3, adr0, m3, plog0, lpt0, ns0, buffered(m4); avol1, rofs0; err1)⟩ ( abs (avol1, buffered(m4), ( (wbuf.content:= copy(buf3, n, wbuf.content, 0, (m2 + n3) % EB_PAGE_SIZE)) .offset:= ((wbuf.content:= copy(buf3, n, wbuf.content, 0, (m2 + n3) % EB_PAGE_SIZE)).offset + align↓(m2 + n3, EB_PAGE_SIZE))) .nbytes:= ((m2 + n3) % EB_PAGE_SIZE), avol0 [buffered(m4).leb, mapped ( avol0[buffered(m4).leb].data + mkempbuf(# buf2 - # avol0[buffered(m4).leb].data) + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n + m2), 0, m2), m2, n), 0, n + m2)) ], rofs) ∧ (rofs0 ↔ rofs) ∧ err = err1), n + m2 = 0, EB_PAGE_SIZE = 0, n3 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, ¬ rofs0, n + m2 ≠ 0, n3 ≠ 0, m2 < EB_PAGE_SIZE, m4 < # avol1, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(n + m2, EB_PAGE_SIZE), is-aligned(# buf2, EB_PAGE_SIZE), n + (m2 + n3) % EB_PAGE_SIZE ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, n3 ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, # buf2 + m2 + n3 ≤ LEB_SIZE, n ≤ # buf3, # buf2 + n + m2 ≤ LEB_SIZE ⊦ ⟨awbuf_write_buf#(n3, buf3, adr0, m3, plog0, lpt0, ns0, buffered(m4); avol1, rofs0; err1)⟩ ( abs (avol1, buffered(m4), mkwbuf(copy(buf3, n, buf1, 0, (m2 + n3) % EB_PAGE_SIZE), # buf2 + n + m2, (m2 + n3) % EB_PAGE_SIZE), avol0[m4, mapped(avol0[m4].data + mkempbuf(# buf2 - # avol0[m4].data) + copy(buf3, 0, copy(buf1, 0, mkbuf(n + m2), 0, m2), m2, n))], false) ∧ ¬ rofs0 ∧ ESUCCESS = err1)

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ m < n → m ≤ n; (s)%n ≠ 0 ⊦ m % n ≤ m; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ mkwbuf(buf, m, m0).nbytes:= m2 = mkwbuf(buf, m, m2); (s)% ⊦ mkwbuf(buf, m, m0).offset:= m1 = mkwbuf(buf, m1, m0); (s)% ⊦ mkwbuf(buf, m, m0).offset = m; (s)% ⊦ mkwbuf(buf, m, m0).content:= buf0 = mkwbuf(buf0, m, m0); (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ m ≤ m + n; (s)% ⊦ m ≤ m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)% ⊦ mkwbuf(buf, m, m0).content = buf; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ buffered(m).leb = m; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)