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Proof step 77 from proof refine-commit (previous step)

# lpt0 = # avol, # lpt2 = # avol, isbuf0 ↔ isbuf, isbuf ↔ false, adr = adr2, adr0 = adr3, bleb = nobuffer, err = ESUCCESS, err = err0, keyset(gch) = gc-heap(lpt2, log1), log = [], log0 = log1, log2 = log1, lpt = lpt0, lpt1 = lpt2, m = m2, maxino = m0, ns = ns2, ns1 = ns4, 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), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, freelist), 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, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [persistence_gc_heap_add_log#(; log0, lpt2, gch); persistence_cleanup_lpt#(adr, m, log, lpt1, ns, bleb, isbuf0; lpt2, freelist, gch, avol)] ( lpt-free-unref(lpt2) ∧ lpt-free-unref(lpt1) ∧ freelist-cons(lpt2, freelist) ∧ log0 = log ∧ bin-heap-inv(gch, lpt2) ∧ keyset(gch) = gc-heap(lpt2, log) ∧ bufs-log-only(bleb, log, lpt2) ∧ # lpt2 = # avol ∧ ¬ dups(log) ∧ log-group-block(log, lpt2) ∧ buf-ro-rw-mode(isbuf0, bleb, lpt2, avol) ∧ lpt-leb-size(lpt2) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt2, lpt1, log) ∧ awbuf-inv(avol, bleb) ∧ # lpt1 = # avol ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → bleb = nobuffer) ∧ (err = ESUCCESS ↔ ¬ isbuf0) → ⟨apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr3, istore0, gstore0, log1, maxino, ns4; pstate, err1)⟩ ( abs-istore(avol, lpt2, istore) ∧ abs-gstore(avol, lpt2, gstore, ginval) ∧ adr3 = adr ∧ maxino = m ∧ log1 = log ∧ ginval < # lpt2 ∧ ns4 = ns ∧ flash-lpt-cons(lpt1, istore0, gstore0) ∧ synced(avol) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ isbuf0) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ ns0 = ns2 ∧ err = err1)), pstate = readonly, dups(log1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
# lpt2 = # avol, # lpt0 = # avol, keyset(gch) = gc-heap(lpt2, log1), log0 = log1, lpt1 = lpt2, 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(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), 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) ⊦ [persistence_gc_heap_add_log#(; log0, lpt2, gch); persistence_cleanup_lpt#(adr2, m2, [], lpt1, ns2, nobuffer, false; lpt2, freelist, gch, avol)] ( lpt-free-unref(lpt2) ∧ lpt-free-unref(lpt1) ∧ freelist-cons(lpt2, freelist) ∧ log0 = [] ∧ bin-heap-inv(gch, lpt2) ∧ keyset(gch) = gc-heap(lpt2, []) ∧ # lpt2 = # avol ∧ lpt-leb-size(lpt2) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt2, lpt1, []) ∧ awbuf-inv(avol, nobuffer) ∧ # lpt1 = # avol → ⟨ns1 := ns2; apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr3, istore0, gstore0, log1, maxino, ns4; pstate, err1)⟩ ( abs-istore(avol, lpt2, istore) ∧ abs-gstore(avol, lpt2, gstore, ginval) ∧ adr3 = adr2 ∧ maxino = m2 ∧ log1 = [] ∧ ginval < # lpt2 ∧ ns4 = ns1 ∧ flash-lpt-cons(lpt1, istore0, gstore0) ∧ pstate = unbuffered ∧ ns0 = ns2 ∧ ESUCCESS = err1))

Rule argument

Additional information

Used simplifier rules: ⊦ unbuffered ≠ readonly; (s)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ awbuf-inv(avol, nobuffer) → (synced(avol) ↔ true); (ss)% ⊦ buf-ro-rw-mode(boolvar, nobuffer, lpt, avol); (s)% ⊦ log-group-block([], lpt); (s)% ⊦ ¬ dups([]); (s)% ⊦ bufs-log-only(nobuffer, nx, lpt); (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)