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Proof step 8 from proof inv-unmap (previous step)

# buf = EB_PAGE_SIZE, # lpt = # avol, buffered(m4) ≠ bleb, m4 < # avol, ebm-vol-inv(avol), bleb ≠ nobuffer → bleb.leb < # avol ∧ wbuf-cons(mkwbuf(buf, m1, m2), avol[bleb.leb], rofs) ⊦ ⟪apersistence_io_unmap#(m4, adr, m, plog, lpt, ns; avol)⟫ ((bleb ≠ nobuffer → bleb.leb < # avol ∧ wbuf-cons(mkwbuf(buf, m1, m2), avol[bleb.leb], rofs)) ∧ ebm-vol-inv(avol) ∧ # lpt = # avol)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 9:
# lpt = # avol, # buf = EB_PAGE_SIZE, m0 = m4, m4 < # avol, ebm-vol-inv(avol), bleb ≠ nobuffer → bleb.leb < # avol ∧ wbuf-cons(mkwbuf(buf, m1, m2), avol[bleb.leb], rofs) ⊦ ⟪if m0 < # avol then avol[m0] := unmapped else abort⟫ ((bleb ≠ nobuffer → bleb.leb < # avol ∧ wbuf-cons(mkwbuf(buf, m1, m2), avol[bleb.leb], rofs)) ∧ ebm-vol-inv(avol) ∧ # lpt = # avol), buffered(m4) = bleb

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_io_unmap# (LNUM, PROOTADR, PMAXINO, PLOG, PLPT, PORPHANS; PVOL) {if LNUM < # PVOL then PVOL[LNUM] := unmapped else abort};