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Proof step 2 from proof abs-buffered (previous step)

avol1[n] = mapped(buf1), n < # avol0, abs(avol0, buffered(n), mkwbuf(buf, m0, m1), avol1, false) ⊦ avol0[n] = mapped(buf1 + subarray(buf, 0, m1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 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 4:
# avol0 = # avol1, avol1[n] = mapped(buf1), n < # avol0, ∀ n0. n0 < # avol0 → (buffered(n0) ≠ buffered(n) → avol0[n0] = avol1[n0]) ∧ (¬ false ∧ buffered(n0) = buffered(n) → avol0[n0] = abs⊕(avol1[n0], mkwbuf(buf, m0, m1))) ∧ ( false ∧ buffered(n0) = buffered(n) → mkwbuf(buf, m0, m1).offset = # avol1[n0].data ∧ avol0[n0] = abs⊕(avol1[n0], mkwbuf(buf, m0, m1)) ∨ mkwbuf(buf, m0, m1).offset < # avol1[n0].data ∧ mkwbuf(buf, m0, m1).offset + mkwbuf(buf, m0, m1).nbytes < # avol1[n0].data ∧ avol0[n0] = avol1[n0] ∧ subarray(mkwbuf(buf, m0, m1).content, 0, mkwbuf(buf, m0, m1).nbytes) = subarray(avol1[n0].data, mkwbuf(buf, m0, m1).offset, mkwbuf(buf, m0, m1).nbytes)) ⊦ avol0[n] = mapped(buf1 + subarray(buf, 0, m1))

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, avol1, mkwbuf(buf, m0, m1), buffered(n), avol0] flags: <all paths>

Additional information

Used terms: false, avol1, mkwbuf(buf, m0, m1), buffered(n), avol0