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Proof step 89 from proof refine-commit (previous step)

# lpt0 = # avol0, # lpt2 = # avol0, # avol = # avol0, # lpt = # avol0, # lpt1 = # avol0, keyset(gch) = gc-heap(lpt2, log1), keyset(gch0) = gc-heap(lpt2, []), keyset(gch1) = gc-heap(cleanup-lpt(lpt), []), ns1 = 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 < # avol0, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), avol-cleanup-lpt-unchanged(avol, avol0, lpt), awbuf-inv(avol, bleb0), awbuf-inv(avol, nobuffer), awbuf-inv(avol0, nobuffer), bin-heap-inv(gch, lpt2), bin-heap-inv(gch0, lpt), bin-heap-inv(gch1, lpt1), 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(cleanup-lpt(lpt), freelist0), id-idx(lpt2, lpt), id-idx(cleanup-lpt(lpt), lpt1), 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-leb-size(cleanup-lpt(lpt)), lpt-ram-flash(lpt2, lpt0, log1), lpt-ram-flash(lpt1, lpt2, []), synced(avol), synced(avol0), 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 < # avol0 ∧ lpt2[n].flags = LP_GROUP_NODES ⊦ ⟨apersistence_commit#(adr2, m2, true; ns2, istore, ginval, gstore, adr3, istore0, gstore0, log1, maxino, ns4; pstate, err1)⟩ ( abs-istore(avol0, cleanup-lpt(lpt), istore) ∧ abs-gstore(avol0, cleanup-lpt(lpt), gstore, ginval) ∧ adr3 = adr2 ∧ maxino = m2 ∧ log1 = [] ∧ ginval < # avol0 ∧ ns4 = ns1 ∧ flash-lpt-cons(lpt2, istore0, gstore0) ∧ pstate = unbuffered ∧ ns0 = ns2 ∧ ESUCCESS = err1), pstate = readonly, dups(log1)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 90:
# lpt1 = # avol0, # lpt = # avol0, # avol = # avol0, # lpt2 = # avol0, # lpt0 = # avol0, isbuf ↔ true, adr = adr3, adr0 = adr2, gstore = gstore1, gstore0 = gstore2, istore = istore1, istore0 = istore2, keyset(gch1) = gc-heap(cleanup-lpt(lpt), []), keyset(gch0) = gc-heap(lpt2, []), keyset(gch) = gc-heap(lpt2, log1), log = log1, m = m2, ns = ns4, ns0 = ns2, ns1 = ns2, remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, dom remove-refsize0(gstore2) ∩ ginval = ∅, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, ginval < # avol0, abs-gstore(avol, lpt2, gstore2, ginval), abs-istore(avol, lpt2, istore2), avol-cleanup-lpt-unchanged(avol, avol0, lpt), awbuf-inv(avol0, nobuffer), awbuf-inv(avol, nobuffer), awbuf-inv(avol, bleb0), bin-heap-inv(gch1, lpt1), 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, istore1, gstore1), freelist-cons(cleanup-lpt(lpt), freelist0), freelist-cons(lpt2, freelist), id-idx(cleanup-lpt(lpt), lpt1), id-idx(lpt2, lpt), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), log-group-block(log1, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(cleanup-lpt(lpt)), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt1, lpt2, []), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), synced(avol), istore1 ⊑ istore2, pstate = unbuffered → bleb0 = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore2, pstate ≠ unbuffered → bleb0 = buffered(pstate.lnum), ∀ n. n ∈ log1 → n < # avol0 ∧ lpt2[n].flags = LP_GROUP_NODES ⊦ ⟨if isbuf ∧ dom remove-refsize0(gstore0) ∩ ginval = ∅ then {fail_or_success#(; ; err); if err = ESUCCESS then {istore0 := remove-refsize0(istore0); istore := istore0; gstore0 := remove-refsize0(gstore0); gstore := gstore0; ginval := ∅; adr := adr0; ns := ns0; log := []; maxino := m; pstate := unbuffered} else pstate := readonly; ns0 := ?} else abort⟩ ( abs-istore(avol0, cleanup-lpt(lpt), istore0) ∧ abs-gstore(avol0, cleanup-lpt(lpt), gstore0, ginval) ∧ adr = adr2 ∧ maxino = m2 ∧ log = [] ∧ ginval < # avol0 ∧ ns = ns1 ∧ flash-lpt-cons(lpt2, istore, gstore) ∧ pstate = unbuffered ∧ ns3 = ns0 ∧ ESUCCESS = err), pstate = readonly, dups(log1)

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_commit# (ROOTADR0, MAXINO0, PSYNCED ; OS0, ISTORE, GINVAL, GSTORE, ROOTADR, ISTORE0, GSTORE0, NL, MAXINO, OS ; PSTATE, ERR ) {if PSYNCED ∧ dom remove-refsize0(GSTORE) ∩ GINVAL = ∅ then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then {ISTORE := remove-refsize0(ISTORE); ISTORE0 := ISTORE; GSTORE := remove-refsize0(GSTORE); GSTORE0 := GSTORE; GINVAL := ∅; ROOTADR := ROOTADR0; OS := OS0; NL := []; MAXINO := MAXINO0; PSTATE := unbuffered} else PSTATE := readonly; OS0 := ?} else abort };