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

# 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 ∈ ginval, ¬ n ∈ nx, isbuf1 → synced(avol) ⊦ ∃ lax, err. (⌊err⌋ ∨ err = ESUCCESS) ∧ ¬ dups(lax1 + lax) ∧ # lax ≤ # lax0 ∧ inv-flashsize(prefixn(# lax, gndx0), lax) ∧ (err = ESUCCESS ↔ # lax = # lax0) ∧ ⟨ax := lax.to-adr(pstate.lnum), err0 := err; gstore[pstate.lnum].gndlist := gstore[pstate.lnum].gndlist + prefixn(# lax, gndx0); gstore[pstate.lnum].ladrlist := gstore[pstate.lnum].ladrlist + lax; 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)

User applied rule exists right

And obtained the following new goals

Proof step 142:
# 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

Rule argument

pos: right 1 terms: lax0, ESUCCESS abort: F discard: T computed: T

Additional information

Used terms: lax0, ESUCCESS