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

gndlist0 + prefixn(# lax1, gndlist) = gndlist1, gstore1 = gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, m2, LEB_SIZE, m1, true)], gstore[maxino] = groupblock(gndlist0, lax0, m2, m0, m1, false), remove-refsize0(istore0) = istore0, remove-refsize0(gstore2) = gstore2, dom gstore2 ∪ elems nx0 = dom gstore ∪ ginval0, elems nx0 ∩ ginval0 = ∅, gstore0 = gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, m2, LEB_SIZE, m1, true)], gndlist ≠ [], # lax1 ≠ # gndlist, m2 ≤ n0, n0 ≤ # gndlist0 + # lax1, btree-inv (rp, adr, gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n0, LEB_SIZE, m1, true)] \ ginval0, istore, istore0, zh, ri1, fi3, ld2), inv(groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n0, LEB_SIZE, m1, true)), flushed(gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n0, LEB_SIZE, m1, true)] \ (ginval0 ∪ elems nx0)), gstore2 \ ginval0 lpt= gstore \ elems nx0, ⌊err1⌋ , maxino ∈ nx0, btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, ri0, fi2, ld1), istore0 ⊑ istore, flushed(istore0), inv(istore0), inv(istore), btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, ri, fi1, ld0), ri-inj(fi0), ri-inj(fi), flushed(gstore \ (ginval0 ∪ elems nx0)), inv(gstore2), inv(gstore \ ginval0), btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, fi, fi0, ld), m0 + gndlist.flashsize ≤ LEB_SIZE, # lax1 < # gndlist, inv-flashsize(prefixn(# lax1, gndlist), lax1), maxino ∈ gstore, m2 ≤ # gndlist0 + # lax1, inv(groupblock(gndlist0, lax0, m2, m0, m1, false)), ¬ maxino ∈ ginval0, ¬ dups(nx0), ¬ dups(lax1), ax = ax2 ⊦ ∃ n. (m2 ≤ n ∧ n ≤ # gndlist1) ∧ ⟨gstore0[maxino].flushindex := n⟩ ( gstore0 = gstore1[maxino, gstore1[maxino].flushindex:= n0] ∧ btree-inv(rp, adr, gstore1[maxino, gstore1[maxino].flushindex:= n0] \ ginval0, istore, istore0, zh, fi, fi0, ld) ∧ ax2 = ax)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
gstore[maxino] = groupblock(gndlist0, lax0, m2, m0, m1, false), remove-refsize0(istore0) = istore0, remove-refsize0(gstore2) = gstore2, dom gstore2 ∪ elems nx0 = dom gstore ∪ ginval0, elems nx0 ∩ ginval0 = ∅, gndlist ≠ [], # lax1 ≠ # gndlist, m2 ≤ n0, n0 ≤ # gndlist0 + # lax1, btree-inv (rp, adr, gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n0, LEB_SIZE, m1, true)] \ ginval0, istore, istore0, zh, ri1, fi3, ld2), inv(groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n0, LEB_SIZE, m1, true)), flushed(gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n0, LEB_SIZE, m1, true)] \ (ginval0 ∪ elems nx0)), gstore2 \ ginval0 lpt= gstore \ elems nx0, ⌊err1⌋ , maxino ∈ nx0, btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, ri0, fi2, ld1), istore0 ⊑ istore, flushed(istore0), inv(istore0), inv(istore), btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, ri, fi1, ld0), ri-inj(fi0), ri-inj(fi), flushed(gstore \ (ginval0 ∪ elems nx0)), inv(gstore2), inv(gstore \ ginval0), btree-inv(rp, adr, gstore \ ginval0, istore, istore0, zh, fi, fi0, ld), m0 + gndlist.flashsize ≤ LEB_SIZE, # lax1 < # gndlist, inv-flashsize(prefixn(# lax1, gndlist), lax1), maxino ∈ gstore, m2 ≤ # gndlist0 + # lax1, inv(groupblock(gndlist0, lax0, m2, m0, m1, false)), ¬ maxino ∈ ginval0, ¬ dups(nx0), ¬ dups(lax1) ⊦ ∃ n. m2 ≤ n ∧ n ≤ # gndlist0 + # lax1 ∧ ⟨gstore0 := gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n, LEB_SIZE, m1, true)]⟩ ( gstore0 = gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n0, LEB_SIZE, m1, true)] ∧ btree-inv (rp, adr, gstore[maxino, groupblock(gndlist0 + prefixn(# lax1, gndlist), lax0 + lax1, n0, LEB_SIZE, m1, true)] \ ginval0, istore, istore0, zh, fi, fi0, ld))

Rule argument

Additional information

Used simplifier rules: insins: ⊦ gstore[n, gblock][n, gblock0] = gstore[n, gblock0]; from specification store[group-store-ablock-store-nat-store]%upd-06: ⊦ groupblock(gndlist, lax, m, m0, m1, boolvar).flushindex:= m2 = groupblock(gndlist, lax, m2, m0, m1, boolvar); from specification ablock[group-store]%At-same: ⊦ gstore[n, gblock][n] = gblock; from specification store[group-store-ablock-store-nat-store]%a: ⊦ (gndlist + gndlist0) + gndlist1 = gndlist + gndlist0 + gndlist1; from specification list[group-store]%prefixn-len-n: n ≤ # gndlist ⊦ # prefixn(n, gndlist) = n; from specification list-prefixn[group-store]%lels-03: ⊦ m < n → m ≤ n; from specification nat%len: ⊦ #(gndlist + gndlist0) = # gndlist + # gndlist0; from specification list[group-store]