[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 50 from proof refine-add-gnds (previous step)

# lpt1 = # avol, # lpt0 = # avol, isbuf ↔ isbuf1, gstore[log1.last] = groupblock(gndx0, lax, m0), lpt1[log1.last] = mklp(m0, m1, LP_GROUP_NODES, m2), avol[log1.last] = mapped(buf), adr = adr0, ax = ax0, gndx = [], istore = istore1, istore0 = istore2, keyset(gch) = gc-heap(lpt1, log1), log = log1, maxino = m, ns = ns0, pstate = journal(log1.last), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, log1.last < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), awbuf-inv(avol, buffered(log1.last)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(log1.last), lpt1, avol), bufs-log-only(buffered(log1.last), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval), inv(groupblock(gndx0, lax, m0)), 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), log1.last ∈ gstore, istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ ⟨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 := ?}⟩ ( abs-gstore(avol, lpt1, gstore, ginval) ∧ (isbuf → synced(avol)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ log1.last = pstate.lnum ∧ [] = ax ∧ ESUCCESS = err0), log1 = [], dups(log1), log1.last ∈ ginval

Heuristic symbolic execution applied rule if negative right

And obtained the following new goals

Proof step 51:
# lpt0 = # avol, # lpt1 = # avol, isbuf ↔ isbuf1, avol[log1.last] = mapped(buf), lpt1[log1.last] = mklp(m0, m1, LP_GROUP_NODES, m2), gstore[log1.last] = groupblock(gndx0, lax, m0), adr = adr0, ax = ax0, gndx = [], istore = istore1, istore0 = istore2, keyset(gch) = gc-heap(lpt1, log1), log = log1, maxino = m, ns = ns0, pstate = journal(log1.last), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, log1.last < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), awbuf-inv(avol, buffered(log1.last)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(log1.last), lpt1, avol), bufs-log-only(buffered(log1.last), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx0, lax, m0)), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), 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), log1.last ∈ gstore, istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ ⟨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 := ?⟩ ( abs-gstore(avol, lpt1, gstore, ginval) ∧ (isbuf → synced(avol)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ log1.last = pstate.lnum ∧ [] = ax ∧ ESUCCESS = err0), log1 = [], dups(log1), log1.last ∈ ginval

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ readonly ≠ journal(m); (s)