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Proof step 36 from proof recovery (previous step)

# avol0 = # avol2, # avol1 = # avol2, # lpt1 = # avol2, # buf = EB_PAGE_SIZE, n < # avol2, awbuf-inv(avol2, bleb0), ebm-vol-inv(avol0), bleb0 ≠ nobuffer → bleb0.leb < # avol2 ∧ wbuf-cons(mkwbuf(buf, m2, m3), avol0[bleb0.leb], rofs0), avol0[n].mapped? → avol1[n] = avol0[n], avol0[n] = unmapped ∧ avol1[n].mapped? → # avol1[n].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n].data, EB_PAGE_SIZE), buffered(n) ≠ bleb0 → avol2[n] = avol0[n], ¬ rofs0 ∧ buffered(n) = bleb0 → avol2[n] = abs⊕(avol0[n], mkwbuf(buf, m2, m3)), rofs0 ∧ buffered(n) = bleb0 → m2 = # avol0[n].data ∧ avol2[n] = abs⊕(avol0[n], mkwbuf(buf, # avol0[n].data, m3)) ∨ m2 < # avol0[n].data ∧ m2 + m3 < # avol0[n].data ∧ avol2[n] = avol0[n] ∧ subarray(buf, 0, m3) = subarray(avol0[n].data, m2, m3) ⊦ (avol2[n].mapped? → avol1[n] = mapped(avol2[n].data.align↓)) ∧ (¬ avol2[n].mapped? ∧ avol1[n].mapped? → # avol1[n].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n].data, EB_PAGE_SIZE))

User applied rule structural induction

And obtained the following new goals

Proof step 37:
# buf = EB_PAGE_SIZE, # lpt1 = # avol2, # avol1 = # avol2, # avol0 = # avol2, mapped(buf0) = avol2[n], n < # avol2, awbuf-inv(avol2, bleb0), ebm-vol-inv(avol0), rofs0 ∧ buffered(n) = bleb0 → m2 = # avol0[n].data ∧ avol2[n] = abs⊕(avol0[n], mkwbuf(buf, # avol0[n].data, m3)) ∨ m2 < # avol0[n].data ∧ m2 + m3 < # avol0[n].data ∧ avol2[n] = avol0[n] ∧ subarray(buf, 0, m3) = subarray(avol0[n].data, m2, m3), ¬ rofs0 ∧ buffered(n) = bleb0 → avol2[n] = abs⊕(avol0[n], mkwbuf(buf, m2, m3)), buffered(n) ≠ bleb0 → avol2[n] = avol0[n], avol0[n] = unmapped ∧ avol1[n].mapped? → # avol1[n].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n].data, EB_PAGE_SIZE), avol0[n].mapped? → avol1[n] = avol0[n], bleb0 ≠ nobuffer → bleb0.leb < # avol2 ∧ wbuf-cons(mkwbuf(buf, m2, m3), avol0[bleb0.leb], rofs0) ⊦ (avol2[n].mapped? → avol1[n] = mapped(avol2[n].data.align↓)) ∧ (¬ avol2[n].mapped? ∧ avol1[n].mapped? → # avol1[n].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n].data, EB_PAGE_SIZE))

Rule argument

term: avol2[n]

Additional information

Used simplifier rules: aleb freely generated by unmapped, mapped;;% ⊦ ¬ unmapped.mapped?; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ mapped(buf).mapped?; (s)% ⊦ aleb.mapped? ↔ aleb ≠ unmapped; (ss)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ mapped(buf).data = buf; (s)%wbuf-cons-mapped: ⊦ wbuf-cons(wbuf, aleb, boolvar) → aleb.mapped?; (forward) from specification wbuf-base%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ unmapped ≠ mapped(buf); (s)% ⊦ buffered(m).leb = m; (s)%⊦ abs⊕(mapped(buf), wbuf) = mapped(buf + subarray(wbuf.content, 0, wbuf.nbytes)); (s)% ⊦ mkwbuf(buf, m, m0).content = buf; (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)