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Proof step 5 from proof refine-is-log-empty (previous step)

# lpt = # avol, # lpt0 = # avol, keyset(gch) = gc-heap(lpt, log0), log = log0, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log0 ∩ ginval = ∅, dom gstore0 ∪ elems log0 = 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, log0, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log0, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log0), istore0 ⊑ istore, isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log0 ≠ [] ∧ pstate.lnum = log0.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf ⊦ ⟨apersistence_is_log_empty#(adr0, istore, istore0, ginval, gstore, gstore0, log0, m, ns0, pstate, isbuf; ; isbuf1)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ (log = [] ↔ isbuf1)), dups(log0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 6:
# lpt0 = # avol, # lpt = # avol, adr = adr0, gstore = gstore1, gstore0 = gstore2, istore = istore1, istore0 = istore2, keyset(gch) = gc-heap(lpt, log0), log = log0, log1 = log0, maxino = m, ns = ns0, remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems log0 ∩ ginval = ∅, dom gstore1 ∪ elems log0 = dom gstore2 ∪ ginval, ginval < # avol, abs-gstore(avol, lpt, gstore2, ginval), abs-istore(avol, lpt, istore2), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log0, lpt), flash-lpt-cons(lpt0, istore1, gstore1), freelist-cons(lpt, freelist), inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval), 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), istore1 ⊑ istore2, pstate = unbuffered → isbuf, pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log0 ≠ [] ∧ pstate.lnum = log0.last ∧ pstate.lnum ∈ gstore2, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf → synced(avol) ⊦ ⟨empty? := log = []⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ (log1 = [] ↔ empty?)), dups(log0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_is_log_empty# (ROOTADR, ISTORE, ISTORE0, GINVAL, GSTORE, GSTORE0, NL, MAXINO, OS, PSTATE, PSYNCED ; ; EMPTY? ) {EMPTY? := NL = []};