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Proof step 49 from proof refine-add-gnds (previous step)

elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, remove-refsize0(gstore2) = gstore2, remove-refsize0(istore0) = istore0, gstore0[maxino] = groupblock(gndlist0, lax0, m, m0, m1, false), gstore1 = gstore0[maxino, groupblock(gndlist0 + prefixn(# lax, gndlist), lax0 + lax, m, LEB_SIZE, m1, true)], # lax ≠ # gndlist, gndlist ≠ [], inv-flashsize(prefixn(# lax, gndlist), lax), # lax < # gndlist, m0 + gndlist.flashsize ≤ LEB_SIZE, btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, fi, fi0, ld), inv(gstore0 \ ginval0), inv(gstore2), flushed(gstore0 \ (ginval0 ∪ elems nx0)), ri-inj(fi), ri-inj(fi0), btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, ri, fi1, ld0), inv(istore), inv(istore0), flushed(istore0), istore0 ⊑ istore, maxino ∈ gstore0, btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, ri0, fi2, ld1), maxino ∈ nx0, inv(groupblock(gndlist0, lax0, m, m0, m1, false)), ⌊err0⌋ , gstore2 \ ginval0 lpt= gstore0 \ elems nx0, flushed(gstore0[maxino, groupblock(gndlist0 + prefixn(# lax, gndlist), lax0 + lax, n, LEB_SIZE, m1, true)] \ (ginval0 ∪ elems nx0)), inv(groupblock(gndlist0 + prefixn(# lax, gndlist), lax0 + lax, n, LEB_SIZE, m1, true)), btree-inv (rp, adr, gstore0[maxino, groupblock(gndlist0 + prefixn(# lax, gndlist), lax0 + lax, n, LEB_SIZE, m1, true)] \ ginval0, istore, istore0, zh, ri1, fi3, ld2), n ≤ # gndlist0 + # lax, m ≤ n, m ≤ # gndlist0 + # lax, ¬ dups(lax), ¬ dups(nx0), ¬ maxino ∈ ginval0, nx = nx0, ax = ax0, gstore = gstore0 ⊦ ⟨if maxino ∈ nx ∧ gstore[maxino].size + gndlist.flashsize ≤ LEB_SIZE ∧ ¬ gstore[maxino].failed then {choose lax, err0 with (⌊err0⌋ ∨ err0 = ESUCCESS) ∧ ¬ dups(gstore[maxino].ladrlist + lax) ∧ # lax ≤ # gndlist ∧ inv-flashsize(prefixn(# lax, gndlist), lax) ∧ (err0 = ESUCCESS ↔ # lax = # gndlist) in {ax := lax.to-adr(maxino), err := err0; gstore[maxino].gndlist := gstore[maxino].gndlist + prefixn(# lax, gndlist); gstore[maxino].ladrlist := gstore[maxino].ladrlist + lax; if err = ESUCCESS then gstore[maxino].size := gstore[maxino].size + gndlist.flashsize else {gstore[maxino].size := LEB_SIZE; gstore[maxino].failed := true; ax := ?}}; choose n with gstore[maxino].flushindex ≤ n ∧ n ≤ # gstore[maxino].gndlist in gstore[maxino].flushindex := n} else abort⟩ ( gstore = gstore1[maxino, gstore1[maxino].flushindex:= n] ∧ btree-inv(rp, adr, gstore1[maxino, gstore1[maxino].flushindex:= n] \ ginval0, istore, istore0, zh, fi, fi0, ld) ∧ ax2 = ax ∧ err0 = err)

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 50:
elems nx0 ∩ ginval0 = ∅, dom gstore2 ∪ elems nx0 = dom gstore0 ∪ ginval0, remove-refsize0(gstore2) = gstore2, remove-refsize0(istore0) = istore0, gstore0[maxino] = groupblock(gndlist0, lax0, m, m0, m1, false), gstore1 = gstore0[maxino, groupblock(gndlist0 + prefixn(# lax, gndlist), lax0 + lax, m, LEB_SIZE, m1, true)], # lax ≠ # gndlist, gndlist ≠ [], inv-flashsize(prefixn(# lax, gndlist), lax), # lax < # gndlist, m0 + gndlist.flashsize ≤ LEB_SIZE, btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, fi, fi0, ld), inv(gstore0 \ ginval0), inv(gstore2), flushed(gstore0 \ (ginval0 ∪ elems nx0)), ri-inj(fi), ri-inj(fi0), btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, ri, fi1, ld0), inv(istore), inv(istore0), flushed(istore0), istore0 ⊑ istore, maxino ∈ gstore0, btree-inv(rp, adr, gstore0 \ ginval0, istore, istore0, zh, ri0, fi2, ld1), maxino ∈ nx0, inv(groupblock(gndlist0, lax0, m, m0, m1, false)), ⌊err0⌋ , gstore2 \ ginval0 lpt= gstore0 \ elems nx0, flushed(gstore0[maxino, groupblock(gndlist0 + prefixn(# lax, gndlist), lax0 + lax, n, LEB_SIZE, m1, true)] \ (ginval0 ∪ elems nx0)), inv(groupblock(gndlist0 + prefixn(# lax, gndlist), lax0 + lax, n, LEB_SIZE, m1, true)), btree-inv (rp, adr, gstore0[maxino, groupblock(gndlist0 + prefixn(# lax, gndlist), lax0 + lax, n, LEB_SIZE, m1, true)] \ ginval0, istore, istore0, zh, ri1, fi3, ld2), n ≤ # gndlist0 + # lax, m ≤ n, m ≤ # gndlist0 + # lax, ¬ dups(lax), ¬ dups(nx0), ¬ maxino ∈ ginval0, nx = nx0, ax = ax0, gstore = gstore0 ⊦ ⟨choose lax, err0 with (⌊err0⌋ ∨ err0 = ESUCCESS) ∧ ¬ dups(gstore[maxino].ladrlist + lax) ∧ # lax ≤ # gndlist ∧ inv-flashsize(prefixn(# lax, gndlist), lax) ∧ (err0 = ESUCCESS ↔ # lax = # gndlist) in {ax := lax.to-adr(maxino), err := err0; gstore[maxino].gndlist := gstore[maxino].gndlist + prefixn(# lax, gndlist); gstore[maxino].ladrlist := gstore[maxino].ladrlist + lax; if err = ESUCCESS then gstore[maxino].size := gstore[maxino].size + gndlist.flashsize else {gstore[maxino].size := LEB_SIZE; gstore[maxino].failed := true; ax := ?}}⟩ ⟨choose n with gstore[maxino].flushindex ≤ n ∧ n ≤ # gstore[maxino].gndlist in gstore[maxino].flushindex := n⟩ ( gstore = gstore1[maxino, gstore1[maxino].flushindex:= n] ∧ btree-inv(rp, adr, gstore1[maxino, gstore1[maxino].flushindex:= n] \ ginval0, istore, istore0, zh, fi, fi0, ld) ∧ ax2 = ax ∧ err0 = err)

Rule argument

Additional information

Used simplifier rules: sel-07: ⊦ groupblock(gndlist, lax, m, m0, m1, boolvar).size = m0; from specification ablock[group-store]%sel-11: ⊦ groupblock(gndlist, lax, m, m0, m1, boolvar).failed ↔ boolvar; from specification ablock[group-store]