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Proof step 49 from proof refine-move-buf (previous step)

# buf = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m5] = mapped(buf0), avol1[n0] = mapped(buf1), avol0[n0] = mapped(buf2), m5 < # avol1, n < # avol1, n0 < # avol1, awbuf-inv(avol1, buffered(n0)), ebm-vol-inv(avol0), is-aligned(# buf1, EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf, m4, 0), mapped(buf2), false), ∀ n. n < # avol1 → (buffered(n) ≠ buffered(n0) → avol1[n] = avol0[n]) ∧ (¬ false ∧ buffered(n) = buffered(n0) → avol1[n] = abs⊕(avol0[n], mkwbuf(buf, m4, 0))) ∧ ( false ∧ buffered(n) = buffered(n0) → mkwbuf(buf, m4, 0).offset = # avol0[n].data ∧ avol1[n] = abs⊕(avol0[n], mkwbuf(buf, m4, 0)) ∨ mkwbuf(buf, m4, 0).offset < # avol0[n].data ∧ mkwbuf(buf, m4, 0).offset + mkwbuf(buf, m4, 0).nbytes < # avol0[n].data ∧ avol1[n] = avol0[n] ∧ subarray(mkwbuf(buf, m4, 0).content, 0, mkwbuf(buf, m4, 0).nbytes) = subarray(avol0[n].data, mkwbuf(buf, m4, 0).offset, mkwbuf(buf, m4, 0).nbytes)) ⊦ avol1[n] = avol0[n], n = m5, n0 = m5

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
# buf = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m5] = mapped(buf0), avol1[n0] = mapped(buf1), avol0[n0] = mapped(buf2), m5 < # avol1, n < # avol1, n0 < # avol1, awbuf-inv(avol1, buffered(n0)), ebm-vol-inv(avol0), is-aligned(# buf1, EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf, m4, 0), mapped(buf2), false), ∀ n1. n1 < # avol1 → (n1 ≠ n0 → avol1[n1] = avol0[n1]) ∧ (n1 = n0 → buf1 = buf2) ⊦ avol1[n] = avol0[n], n = m5, n0 = m5

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ buf + mkbuf(0) = buf; (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ mkwbuf(buf, m, m0).content = buf; (s)%⊦ abs⊕(mapped(buf), wbuf) = mapped(buf + subarray(wbuf.content, 0, wbuf.nbytes)); (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)