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Proof step 54 from proof inv-commit (previous step)

# lpt0 = # avol, # lpt2 = # avol, keyset(gch0) = gc-heap(lpt2, []), keyset(gch) = gc-heap(lpt2, log1), awbuf-inv(avol, bleb0), awbuf-inv(avol, nobuffer), bin-heap-inv(gch0, lpt), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), freelist-cons(lpt2, freelist), id-idx(lpt2, lpt), 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), ¬ dups(log1), ∀ n. n ∈ log1 → n < # avol ∧ lpt2[n].flags = LP_GROUP_NODES ⊦ ⟪persistence_cleanup_lpt#(adr0, m0, [], lpt2, ns0, 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)

User applied rule insert program lemma

And obtained the following new goals

Proof step 55:
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 56:
# lpt2 = # avol, # lpt0 = # avol, # avol = # lpt, boolvar0 ↔ false, adr1 = adr0, 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 = m0, ns1 = ns0, 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), freelist-cons(lpt2, freelist), freelist-cons(lpt, freelist), id-idx(lpt2, lpt), 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), ∀ n. n ∈ log1 → n < # avol ∧ lpt2[n].flags = LP_GROUP_NODES ⊦ [persistence_cleanup_lpt#(adr0, m0, [], lpt2, ns0, 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), dups(log1)

Rule argument

spec: <toplevel> 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, ns0, lpt2, [], m0, adr0, 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)