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Proof step 83 from proof refine-commit (previous step)

# lpt2 = # avol, # lpt0 = # avol, keyset(gch0) = gc-heap(lpt2, []), keyset(gch) = gc-heap(lpt2, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, dom remove-refsize0(gstore) ∩ ginval = ∅, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, pstate ≠ readonly, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, nobuffer), awbuf-inv(avol, bleb0), bin-heap-inv(gch0, lpt), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, freelist), id-idx(lpt2, lpt), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log1), synced(avol), istore0 ⊑ istore, ¬ dups(log1), pstate = unbuffered → bleb0 = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate ≠ unbuffered → bleb0 = buffered(pstate.lnum), ∀ n. n ∈ log1 → n < # avol ∧ lpt2[n].flags = LP_GROUP_NODES ⊦ [persistence_cleanup_lpt#(adr2, m2, [], lpt2, ns2, nobuffer, false; lpt, freelist, gch0, avol)] ( lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch0, lpt) ∧ keyset(gch0) = gc-heap(lpt, []) ∧ # lpt = # avol ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt2, []) ∧ awbuf-inv(avol, nobuffer) ∧ # lpt2 = # avol → ⟨ns1 := ns2; apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr3, istore0, gstore0, log1, maxino, ns4; pstate, err1)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ adr3 = adr2 ∧ maxino = m2 ∧ log1 = [] ∧ ginval < # lpt ∧ ns4 = ns1 ∧ flash-lpt-cons(lpt2, istore0, gstore0) ∧ pstate = unbuffered ∧ ns0 = ns2 ∧ ESUCCESS = err1))

User applied rule insert program lemma

And obtained the following new goals

Proof step 84:
lpt0 = lpt, avol0 = avol, # avol = # lpt, awbuf-inv(avol, nobuffer), freelist-cons(lpt, freelist), bin-heap-inv(gch, lpt), keyset(gch) = gc-heap(lpt, []), synced(avol) ⊦ ⟪persistence_cleanup_lpt#(adr, m0, log, lpt1, ns, nobuffer, boolvar; lpt, freelist, gch, avol)⟫ ( id-idx(cleanup-lpt(lpt0), lpt) ∧ avol-cleanup-lpt-unchanged(avol0, avol, lpt0) ∧ freelist-cons(lpt, freelist) ∧ awbuf-inv(avol, nobuffer) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, []) ∧ synced(avol))
Proof step 85:
# lpt0 = # avol, # lpt2 = # avol, # avol = # lpt, boolvar0 ↔ false, adr0 = adr2, avol = avol, avol1 = avol, keyset(gch) = gc-heap(lpt2, log1), keyset(gch0) = gc-heap(lpt2, []), keyset(gch0) = gc-heap(lpt, []), log0 = [], lpt = lpt, lpt3 = lpt, lpt4 = lpt2, m = m2, ns3 = ns2, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom remove-refsize0(gstore) ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, bleb0), awbuf-inv(avol, nobuffer), bin-heap-inv(gch, lpt2), bin-heap-inv(gch0, lpt), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, freelist), freelist-cons(lpt, freelist), id-idx(lpt2, lpt), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log1), synced(avol), istore0 ⊑ istore, pstate ≠ unbuffered → bleb0 = buffered(pstate.lnum), pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate = unbuffered → bleb0 = nobuffer, ∀ n. n ∈ log1 → n < # avol ∧ lpt2[n].flags = LP_GROUP_NODES ⊦ [persistence_cleanup_lpt#(adr2, m2, [], lpt2, ns2, nobuffer, false; lpt, freelist, gch0, avol)] ( id-idx(cleanup-lpt(lpt3), lpt) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt3) ∧ freelist-cons(lpt, freelist) ∧ awbuf-inv(avol, nobuffer) ∧ bin-heap-inv(gch0, lpt) ∧ keyset(gch0) = gc-heap(lpt, []) ∧ synced(avol) → lpt-free-unref(lpt) ∧ freelist-cons(lpt, freelist) ∧ bin-heap-inv(gch0, lpt) ∧ keyset(gch0) = gc-heap(lpt, []) ∧ # lpt = # avol ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt, lpt2, []) ∧ awbuf-inv(avol, nobuffer) ∧ # lpt2 = # avol → ⟨ns1 := ns2; apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr3, istore0, gstore0, log1, maxino, ns4; pstate, err1)⟩ ( abs-istore(avol, lpt, istore) ∧ abs-gstore(avol, lpt, gstore, ginval) ∧ adr3 = adr2 ∧ maxino = m2 ∧ log1 = [] ∧ ginval < # lpt ∧ ns4 = ns1 ∧ flash-lpt-cons(lpt2, istore0, gstore0) ∧ pstate = unbuffered ∧ ns0 = ns2 ∧ ESUCCESS = err1)), pstate = readonly, dups(log1)

Rule argument

spec: persistence-asm name: prepost-cleanup-lpt seq: lpt0 = lpt, avol0 = avol, # avol = # lpt, awbuf-inv(avol, nobuffer), freelist-cons(lpt, freelist), bin-heap-inv(gch, lpt), keyset(gch) = gc-heap(lpt, []), synced(avol) ⊦ ⟪persistence_cleanup_lpt# (adr, m0, log, lpt1, ns, nobuffer, boolvar ; lpt, freelist, gch, avol)⟫ ( id-idx(cleanup-lpt(lpt0), lpt) ∧ avol-cleanup-lpt-unchanged(avol0, avol, lpt0) ∧ freelist-cons(lpt, freelist) ∧ awbuf-inv(avol, nobuffer) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, []) ∧ synced(avol)) subst: [boolvar, ns, lpt1, log, m0, adr, avol, gch, freelist, lpt, lpt0, avol0] → [false, ns2, lpt2, [], m2, adr2, avol, gch0, freelist, lpt, lpt, avol] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n = # lpt0 ∧ id-idx(lpt0, lpt1) → (n = # lpt1 ↔ true); (ss)%⊦ id-idx(lpt0, lpt1) → (freelist-cons(lpt1, freelist) ↔ freelist-cons(lpt0, freelist)); (s)% ⊦ id-idx(lpt0, lpt1) → gc-heap(lpt1, nx) = gc-heap(lpt0, nx); (s)% ⊦ awbuf-inv(avol, nobuffer) → (synced(avol) ↔ true); (ss)