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Proof step 2 from proof refine-requires-commit (previous step)

# lpt0 = # avol, # lpt = # avol, pstate = readonly ↔ isbuf0, adr = adr0, keyset(gch) = gc-heap(lpt, log0), log = log0, log0 = log1, m0 = LEB_SIZE, maxino = m, ns = ns0, ginval < # lpt, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf0, bleb, lpt, avol), bufs-log-only(bleb, log0, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv-index(istore, istore0), inv-journal(log, gstore, gstore0, ginval), inv-state(pstate, log, gstore, istore, isbuf), log-group-block(log0, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log0), pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol) ⊦ ⟪persistence_requires_commit#(adr0, m, log1, avol, lpt0, ns0, bleb, isbuf0; ; isbuf1)⟫ ⟨apersistence_requires_commit#(adr, istore, istore0, ginval, gstore, gstore0, log, maxino, ns, pstate, isbuf; ; isbuf2)⟩ ( ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ adr = adr0 ∧ maxino = m ∧ log = log0 ∧ ginval < # lpt ∧ ns = ns0 ∧ flash-lpt-cons(lpt0, istore0, gstore0) ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum))) ∧ (isbuf1 ↔ isbuf2)), dups(log0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# lpt = # avol, # lpt0 = # avol, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), istore0 ⊑ istore, ¬ dups(log1), isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf ⊦ ⟪persistence_requires_commit#(adr0, m, log1, avol, lpt0, ns0, bleb, pstate = readonly; ; isbuf1)⟫ ⟨apersistence_requires_commit#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0, pstate, isbuf; ; isbuf2)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ (isbuf1 ↔ isbuf2))

Rule argument

Additional information

Used simplifier rules: ⊦ inv-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)%⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)%⊦ inv-state(pstate, nx, gstore, istore, syn) ↔ ( pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn); (s)