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Proof step 2 from proof recovery (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, pstate0 = readonly ↔ isbuf1, adr0 = adr1, adr2 = adr1, adr3 = adr4, keyset(gch) = gc-heap(lpt1, log3), log0 = log1, log2 = log3, log3 = log1, log5 = log6, lpt = lpt0, m0 = m1, m2 = m1, m3 = LEB_SIZE, m4 = m5, ns1 = ns2, ns4 = ns2, ns5 = ns6, ns3 < # lpt1, abs-gstore(avol0, lpt1, gstore1, ns3), abs-istore(avol0, lpt1, istore1), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(isbuf1, bleb, lpt1, avol0), bufs-log-only(bleb, log3, lpt1), flash-lpt-cons(lpt0, istore2, gstore2), freelist-cons(lpt1, log4), inv-index(istore1, istore2), inv-journal(log2, gstore1, gstore2, ns3), inv-state(pstate0, log2, gstore1, istore1, isbuf0), log-group-block(log3, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log3), synced(avol0), avol ↓ avol0, pstate0 ≠ unbuffered ∧ pstate0 ≠ readonly → bleb = buffered(pstate0.lnum), pstate0 = unbuffered → bleb = nobuffer, isbuf0 → synced(avol0) ⊦ ⟪persistence_recover#(; adr3, m4, log5, ns5, log7, lpt2, freelist, gch0, m6, adr0, m0, log0, avol, lpt, ns1, bleb0, isbuf2; err)⟫ ( ( err = ESUCCESS → (∃ adr, istore, istore0, ginval, gstore, gstore0, log, maxino, ns, pstate, isbuf. ( adr = adr2 ∧ istore = remove-refsize0(crash(istore1, istore2)) ∧ istore0 = istore2 ∧ ginval = ns3 ∧ gstore = crash(gstore1, gstore2, ns3, log2) ∧ gstore0 = gstore2 ∧ log = log2 ∧ maxino = m2 ∧ ns = ns4) ∧ ⟨apersistence_recover#(; adr4, m5, log6, ns6, adr, log, maxino, ns, istore, istore0, ginval, gstore, gstore0; pstate, isbuf, err0)⟩ ( ( abs-istore(avol, lpt2, istore) ∧ abs-gstore(avol, lpt2, gstore, ginval) ∧ adr = adr0 ∧ maxino = m0 ∧ log = log7 ∧ ginval < # lpt2 ∧ ns = ns1 ∧ flash-lpt-cons(lpt, istore0, gstore0) ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb0 = nobuffer) ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb0 = buffered(pstate.lnum))) ∧ adr3 = adr4 ∧ m4 = m5 ∧ log5 = log6 ∧ ns5 = ns6 ∧ err = err0))) ∧ ( err ≠ ESUCCESS → (∀ adr, istore, istore0, ns, gstore, gstore0, log, m, ns0, pstate, isbuf. ⟨apersistence_recover# (; adr4, m5, log6, ns6, adr5, log8, maxino0, ns7, istore3, istore4, ginval0, gstore3, gstore4; pstate1, isbuf3, err0)⟩ ( adr = adr5 ∧ istore = istore3 ∧ istore0 = istore4 ∧ ns = ginval0 ∧ gstore = gstore3 ∧ gstore0 = gstore4 ∧ log = log8 ∧ m = maxino0 ∧ ns0 = ns7 ∧ pstate = pstate1 ∧ (isbuf ↔ isbuf3) ∧ adr3 = adr4 ∧ m4 = m5 ∧ log5 = log6 ∧ ns5 = ns6 ∧ err = err0)))), dups(log3)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# lpt1 = # avol0, # lpt0 = # avol0, adr0 = adr1, adr3 = adr4, keyset(gch) = gc-heap(lpt1, log1), log0 = log1, log5 = log6, m0 = m1, m4 = m5, ns1 = ns2, ns5 = ns6, remove-refsize0(gstore2) = gstore2, remove-refsize0(istore2) = istore2, elems log1 ∩ ns3 = ∅, dom gstore2 ∪ elems log1 = dom gstore1 ∪ ns3, ns3 < # avol0, abs-gstore(avol0, lpt1, gstore1, ns3), abs-istore(avol0, lpt1, istore1), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(pstate0 = readonly, bleb, lpt1, avol0), bufs-log-only(bleb, log1, lpt1), flash-lpt-cons(lpt0, istore2, gstore2), freelist-cons(lpt1, log4), inv(gstore1 \ ns3), inv(gstore2), inv(istore1), inv(istore2), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), synced(avol0), avol ↓ avol0, istore2 ⊑ istore1, ¬ dups(log1), pstate0 = unbuffered → bleb = nobuffer, pstate0 ≠ unbuffered ∧ pstate0 ≠ readonly → bleb = buffered(pstate0.lnum), pstate0.journal? → log1 ≠ [] ∧ pstate0.lnum = log1.last ∧ pstate0.lnum ∈ gstore1, pstate0.index? → pstate0.lnum ∈ istore1, pstate0 = unbuffered → isbuf0 ⊦ ⟪persistence_recover#(; adr3, m4, log5, ns5, log7, lpt2, freelist, gch0, m6, adr0, m0, log0, avol, lpt0, ns1, bleb0, isbuf2; err)⟫ ( ( err = ESUCCESS → ⟨istore := remove-refsize0(crash(istore1, istore2)), gstore := crash(gstore1, gstore2, ns3, log1); apersistence_recover#(; adr4, m5, log6, ns6, adr1, log1, m1, ns2, istore, istore2, ns3, gstore, gstore2; pstate, isbuf, err0)⟩ ( abs-istore(avol, lpt2, istore) ∧ abs-gstore(avol, lpt2, gstore, ns3) ∧ adr1 = adr0 ∧ m1 = m0 ∧ log1 = log7 ∧ ns3 < # lpt2 ∧ ns2 = ns1 ∧ flash-lpt-cons(lpt0, istore2, gstore2) ∧ (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb0 = nobuffer) ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb0 = buffered(pstate.lnum)) ∧ adr3 = adr4 ∧ m4 = m5 ∧ log5 = log6 ∧ ns5 = ns6 ∧ ESUCCESS = err0)) ∧ ( err ≠ ESUCCESS → (∀ adr, istore, istore0, ns, gstore, gstore0, log, m, ns0, pstate, isbuf. ⟨apersistence_recover# (; adr4, m5, log6, ns6, adr5, log8, maxino0, ns7, istore3, istore4, ginval0, gstore3, gstore4; pstate1, isbuf3, err0)⟩ ( adr = adr5 ∧ istore = istore3 ∧ istore0 = istore4 ∧ ns = ginval0 ∧ gstore = gstore3 ∧ gstore0 = gstore4 ∧ log = log8 ∧ m = maxino0 ∧ ns0 = ns7 ∧ pstate = pstate1 ∧ (isbuf ↔ isbuf3) ∧ adr3 = adr4 ∧ m4 = m5 ∧ log5 = log6 ∧ ns5 = ns6 ∧ err = err0))))

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)