[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 32 from proof inv-truncate (previous step)

gstore2[m] = groupblock(gndx, lax, m2), dom gstore2 = dom gstore3, fi = fi2, fi0 = fi1 \ datakeys(key, n0, fi1), gstore = gstore2, gstore0 = gstore1, lnum = m, n = m2 - m1, remove-refsize0(gstore1) = gstore1, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore[lnum, gstore[lnum].ref-size:= n] ∪ jro, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore2 =○refsize gstore3, inv(gstore[lnum, gstore[lnum].ref-size:= n] \ jro), inv(gstore2 \ jro), inv(gstore1), inv(gstore3 \ jro), refsize-cons(gstore2, range(fi1 \ datakeys(key, n0, fi1)) ∪ as0), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi1), lnum ∈ gstore, m ∈ gstore2, @(m, m0, m1) ∈ as0, pmaxino ≤ jmaxino, m2 ≥ m1, as0.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro) ⊦ ⟪as := as0 -- @(m, m0, m1)⟫ ( (jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore[lnum, gstore[lnum].ref-size:= n], jro)) ∧ dom gstore[lnum, gstore[lnum].ref-size:= n] = dom gstore3 ∧ as ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅ ∧ as.lebs ⊆ dom gstore[lnum, gstore[lnum].ref-size:= n] ∧ refsize-cons(gstore[lnum, gstore[lnum].ref-size:= n], range(fi1 \ datakeys(key, n0, fi1)) ∪ as) ∧ gstore[lnum, gstore[lnum].ref-size:= n] =○refsize gstore3 ∧ # as < # as0), # as0 = 0, as0 = ∅, pmaxino = 0, dups(nx)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

Additional information