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Proof step 38 from proof recovery (previous step)

# 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 ∧ mapped(buf0) = abs⊕(avol0[n], mkwbuf(buf, # avol0[n].data, m3)) ∨ m2 < # avol0[n].data ∧ m2 + m3 < # avol0[n].data ∧ mapped(buf0) = avol0[n] ∧ subarray(buf, 0, m3) = subarray(avol0[n].data, m2, m3), ¬ rofs0 ∧ buffered(n) = bleb0 → mapped(buf0) = abs⊕(avol0[n], mkwbuf(buf, m2, m3)), buffered(n) ≠ bleb0 → mapped(buf0) = 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) ⊦ avol1[n] = mapped(buf0.align↓)

User applied rule structural induction

And obtained the following new goals

Proof step 39:
# avol0 = # avol2, # avol1 = # avol2, # lpt1 = # avol2, # buf = EB_PAGE_SIZE, mapped(buf0) = avol2[n], mapped(buf1) = avol0[n], 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 → mapped(buf0) = avol0[n], ¬ rofs0 ∧ buffered(n) = bleb0 → mapped(buf0) = abs⊕(avol0[n], mkwbuf(buf, m2, m3)), rofs0 ∧ buffered(n) = bleb0 → m2 = # avol0[n].data ∧ mapped(buf0) = abs⊕(avol0[n], mkwbuf(buf, # avol0[n].data, m3)) ∨ m2 < # avol0[n].data ∧ m2 + m3 < # avol0[n].data ∧ mapped(buf0) = avol0[n] ∧ subarray(buf, 0, m3) = subarray(avol0[n].data, m2, m3) ⊦ avol1[n] = mapped(buf0.align↓)

Rule argument

term: avol0[n]

Additional information

Used simplifier rules: aleb freely generated by unmapped, mapped;;% ⊦ ¬ unmapped.mapped?; (s)% ⊦ unmapped ≠ mapped(buf); (s)% ⊦ abs⊕(unmapped, wbuf) = unmapped; (s)