[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 36 from proof refine-add-gnds (previous step)

# lpt0 = # avol, # lpt1 = # avol, lpt1[bleb.leb] = mklp(m3, m1, lpf, m2), ax = ax0, keyset(gch) = gc-heap(lpt1, log1), pstate = readonly, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(true, bleb, lpt1, avol), bufs-log-only(bleb, log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log1), istore0 ⊑ istore, ¬ dups(log1), isbuf1 → synced(avol) ⊦ ⟨apersistence_add_gnds#(gndx0, adr0, istore, istore0, ginval, gstore0, log1, m, ns0; ax0, gstore, pstate, isbuf1; err0)⟩ (abs-gstore(avol, lpt1, gstore, ginval) ∧ (isbuf1 → synced(avol)) ∧ pstate = readonly ∧ ax = ax0 ∧ EROFS = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 37:
# lpt1 = # avol, # lpt0 = # avol, isbuf ↔ isbuf1, lpt1[bleb.leb] = mklp(m3, m1, lpf, m2), adr = adr0, ax = ax0, ax1 = ax0, gndx = gndx0, istore = istore1, istore0 = istore2, keyset(gch) = gc-heap(lpt1, log1), log = log1, maxino = m, ns = ns0, pstate = readonly, remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(true, bleb, lpt1, avol), bufs-log-only(bleb, log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log1), istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ ⟨if pstate.journal? ∨ pstate = readonly then if pstate = readonly then err0 := EROFS else {choose lax, err with (⌊err⌋ ∨ err = ESUCCESS) ∧ ¬ dups(gstore[pstate.lnum].ladrlist + lax) ∧ # lax ≤ # gndx ∧ inv-flashsize(prefixn(# lax, gndx), lax) ∧ (err = ESUCCESS ↔ # lax = # gndx) in {ax := lax.to-adr(pstate.lnum), err0 := err; gstore[pstate.lnum].gndlist := gstore[pstate.lnum].gndlist + prefixn(# lax, gndx); gstore[pstate.lnum].ladrlist := gstore[pstate.lnum].ladrlist + lax; if err0 ≠ ESUCCESS then ax := ?, pstate := readonly}; isbuf := ?} else abort⟩ (abs-gstore(avol, lpt1, gstore, ginval) ∧ (isbuf → synced(avol)) ∧ pstate = readonly ∧ ax1 = ax ∧ EROFS = err0), dups(log1)

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_add_gnds# (GNDLIST, ROOTADR, ISTORE, ISTORE0, GINVAL, GSTORE0, NL, MAXINO, OS ; ADRLIST, GSTORE, PSTATE, PSYNCED ; ERR ) {if PSTATE.journal? ∨ PSTATE = readonly then if PSTATE = readonly then ERR := EROFS else {choose LADRLIST, ERR0 with (⌊ERR0⌋ ∨ ERR0 = ESUCCESS) ∧ ¬ dups(GSTORE[PSTATE.lnum].ladrlist + LADRLIST) ∧ # LADRLIST ≤ # GNDLIST ∧ inv-flashsize (prefixn(# LADRLIST, GNDLIST), LADRLIST) ∧ (ERR0 = ESUCCESS ↔ # LADRLIST = # GNDLIST) in {ADRLIST := LADRLIST.to-adr(PSTATE.lnum), ERR := ERR0; GSTORE[PSTATE.lnum].gndlist := GSTORE[PSTATE.lnum].gndlist + prefixn(# LADRLIST, GNDLIST); GSTORE[PSTATE.lnum].ladrlist := GSTORE[PSTATE.lnum].ladrlist + LADRLIST; if ERR ≠ ESUCCESS then ADRLIST := ?, PSTATE := readonly}; PSYNCED := ?} else abort };