[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 250 from proof refine-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol1[m4] = mapped(buf0), avol0[m4] = mapped(buf2), m4 < # avol1, m2 + n < EB_PAGE_SIZE, 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), # buf2 + m2 + n ≤ LEB_SIZE, n ≤ # buf, # buf0 + n ≤ LEB_SIZE ⊦ abs(avol1[m4, mapped(buf0 + subarray(buf, 0, n))], buffered(m4), mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n), avol0, false)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 251:
⊦ abs(avol0, bleb, wbuf, avol1, rofs) ↔ # avol0 = # avol1 ∧ (∀ n. n < # avol0 → (buffered(n) ≠ bleb → avol0[n] = avol1[n]) ∧ (¬ rofs ∧ buffered(n) = bleb → avol0[n] = abs⊕(avol1[n], wbuf)) ∧ ( rofs ∧ buffered(n) = bleb → wbuf.offset = # avol1[n].data ∧ avol0[n] = abs⊕(avol1[n], wbuf) ∨ wbuf.offset < # avol1[n].data ∧ wbuf.offset + wbuf.nbytes < # avol1[n].data ∧ avol0[n] = avol1[n] ∧ subarray(wbuf.content, 0, wbuf.nbytes) = subarray(avol1[n].data, wbuf.offset, wbuf.nbytes)))
Proof step 252:
# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), avol1[m4] = mapped(buf0), m2 < EB_PAGE_SIZE, m2 + n < 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(# buf2, EB_PAGE_SIZE), # buf0 + n ≤ LEB_SIZE, n ≤ # buf, # buf2 + m2 + n ≤ LEB_SIZE ⊦ # avol1[m4, mapped(buf0 + subarray(buf, 0, n))] = # avol0 ∧ (∀ n0. n0 < # avol1[m4, mapped(buf0 + subarray(buf, 0, n))] → (buffered(n0) ≠ buffered(m4) → avol1[m4, mapped(buf0 + subarray(buf, 0, n))][n0] = avol0[n0]) ∧ ( ¬ false ∧ buffered(n0) = buffered(m4) → avol1[m4, mapped(buf0 + subarray(buf, 0, n))][n0] = abs⊕(avol0[n0], mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n))) ∧ ( false ∧ buffered(n0) = buffered(m4) → mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).offset = # avol0[n0].data ∧ avol1[m4, mapped(buf0 + subarray(buf, 0, n))][n0] = abs⊕(avol0[n0], mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n)) ∨ mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).offset < # avol0[n0].data ∧ mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).offset + mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).nbytes < # avol0[n0].data ∧ avol1[m4, mapped(buf0 + subarray(buf, 0, n))][n0] = avol0[n0] ∧ subarray (mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).content, 0, mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).nbytes) = subarray (avol0[n0].data, mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).offset, mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).nbytes)))

Rule argument

spec: wbuf-abs name: abs-def seq: ⊦ abs(avol0, bleb, wbuf, avol1, rofs) ↔ # avol0 = # avol1 ∧ (∀ n. n < # avol0 → (buffered(n) ≠ bleb → avol0[n] = avol1[n]) ∧ ( ¬ rofs ∧ buffered(n) = bleb → avol0[n] = abs⊕(avol1[n], wbuf)) ∧ ( rofs ∧ buffered(n) = bleb → wbuf.offset = # avol1[n].data ∧ avol0[n] = abs⊕(avol1[n], wbuf) ∨ wbuf.offset < # avol1[n].data ∧ wbuf.offset + wbuf.nbytes < # avol1[n].data ∧ avol0[n] = avol1[n] ∧ subarray(wbuf.content, 0, wbuf.nbytes) = subarray (avol1[n].data, wbuf.offset, wbuf.nbytes))) subst: [rofs, avol1, wbuf, bleb, avol0] → [false, avol0, mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n), buffered(m4), avol1[m4, mapped(buf0 + subarray(buf, 0, n))]] flags: <all paths>

Additional information

Used terms: false, avol0, mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n), buffered(m4), avol1[m4, mapped(buf0 + subarray(buf, 0, n))]