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

# gndx0 = # lax0, # buf0 = gndx0.flashsize, # lpt0 = # avol, # lpt1 = # avol, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, gstore[n] = groupblock(gndx1, lax1, m1), avol[n] = mapped(buf1), lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), keyset(gch) = gc-heap(lpt1, nx + n '), pstate = journal(n), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, ginval ∩ elems nx = ∅, ginval < # avol, n < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol[n, mapped(buf1 + buf0)], buffered(n)), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(groupblock(gndx1, lax1, m1)), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, isbuf1 → synced(avol) ⊦ (⌊ESUCCESS⌋ ∨ ESUCCESS = ESUCCESS) ∧ ¬ dups(lax1 + lax0) ∧ # lax0 ≤ # lax0 ∧ inv-flashsize(prefixn(# lax0, gndx0), lax0) ∧ (ESUCCESS = ESUCCESS ↔ # lax0 = # lax0) ∧ ⟨ax := lax0.to-adr(pstate.lnum), err0 := ESUCCESS; gstore[pstate.lnum].gndlist := gstore[pstate.lnum].gndlist + prefixn(# lax0, gndx0); gstore[pstate.lnum].ladrlist := gstore[pstate.lnum].ladrlist + lax0; if err0 ≠ ESUCCESS then ax := ?, pstate := readonly; isbuf1 := ?⟩ ( abs-gstore (avol[pstate.lnum, mapped(avol[pstate.lnum].data + buf0)], lpt1 [pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, lpt1[pstate.lnum].size + gndx0.flashsize, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx) ], gstore, ginval) ∧ (isbuf1 → is-aligned(# avol[pstate.lnum].data + # buf0, EB_PAGE_SIZE)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ n = pstate.lnum ∧ lax0.to-adr(pstate.lnum) = ax ∧ ESUCCESS = err0), gndx0 = [], dups(nx), n ∈ ginval, n ∈ nx

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 143:
# lpt1 = # avol, # lpt0 = # avol, # buf0 = gndx0.flashsize, # gndx0 = # lax0, (elems nx ∪ dom gstore0) ++ n = dom gstore ∪ ginval, lpt1[n] = mklp(m1, # buf1, LP_GROUP_NODES, m2), avol[n] = mapped(buf1), gstore[n] = groupblock(gndx1, lax1, m1), keyset(gch) = gc-heap(lpt1, nx + n '), pstate = journal(n), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, ginval ∩ elems nx = ∅, gndx0 ≠ [], n < # avol, ginval < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore2), abs-nodes(buf0, # buf1, gndx0, lax0, false), awbuf-inv(avol, buffered(n)), awbuf-inv(avol[n, mapped(buf1 + buf0)], buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), nx + n ', lpt1), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt1, freelist), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval), inv(groupblock(gndx1, lax1, m1)), log-group-block(nx + n ', lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, nx + n '), n ∈ gstore, # buf1 + gndx0.flashsize ≤ LEB_SIZE, istore1 ⊑ istore2, ¬ dups(nx), ¬ n ∈ nx, ¬ n ∈ ginval, isbuf1 → synced(avol) ⊦ ¬ dups(lax1 + lax0) ∧ ⟨ax := lax0.to-adr(pstate.lnum), err0 := ESUCCESS; gstore[pstate.lnum].gndlist := gstore[pstate.lnum].gndlist + prefixn(# lax0, gndx0); gstore[pstate.lnum].ladrlist := gstore[pstate.lnum].ladrlist + lax0; if err0 ≠ ESUCCESS then ax := ?, pstate := readonly; isbuf1 := ?⟩ ( abs-gstore (avol[pstate.lnum, mapped(avol[pstate.lnum].data + buf0)], lpt1 [pstate.lnum, mklp(lpt1[pstate.lnum].ref-size, lpt1[pstate.lnum].size + gndx0.flashsize, lpt1[pstate.lnum].flags, lpt1[pstate.lnum].gcheapidx) ], gstore, ginval) ∧ (isbuf1 → is-aligned(# avol[pstate.lnum].data + # buf0, EB_PAGE_SIZE)) ∧ pstate ≠ unbuffered ∧ pstate ≠ readonly ∧ n = pstate.lnum ∧ lax0.to-adr(pstate.lnum) = ax ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ abs-nodes(buf, m, gndx, lax, weak) → inv-flashsize(gndx, lax); (s)%# gndx ≤ m ⊦ prefixn(m, gndx) = gndx; (s)% ⊦ ¬ natkey < natkey; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ m; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)