[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 71 from proof inv-gc-update-index (previous step)

# ax3 = # ndx2, # ax2 = # ndx1, jvalid ↔ jvalid0, gstore3[@(m, m0, m1)] = mkgnode(nd, m2, boolvar, boolvar0), fi2[ndx2.keys, ax3][nd.key] = @(m3, m4, m5), abs-log(nx, gstore3 ↓) = abs-log(nx, gstore2 ↓), dom gstore3 = dom gstore2, fi = fi1, fi0 = fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)], gstore = gstore1, gstore0 = gstore3, jro = jro0, lnum = m3, nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro0), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, range fi2 ∩ ax2.toSet = ∅, range fi2 ∩ ax3.toSet = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, fi1.inos < pmaxino, fi2[ndx2.keys, ax3].inos < jmaxino, p_os < pmaxino, fi2.inos < jmaxino1, jro1 < jmaxino1, inv(gstore3 \ jro0), inv(gstore1), inv(gstore2 \ jro0), key-cons(nd.key, nd), key-cons(ndx2), key-cons(ndx1), nodes-cons(ax3 + @(m, m0, m1) ' + ax2, ndx2 + nd ' + ndx1, gstore2, jro0), nodes-cons(ax2, ndx1, gstore3, jro0), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, range fi2[ndx2.keys, ax3]), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2), nd.key ∈ fi2[ndx2.keys, ax3], @(m, m0, m1) ∈ gstore3, nd.key ∈ fi2, m3 ∈ gstore2, pmaxino ≤ jmaxino, pmaxino ≤ jmaxino1, jmaxino1 ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2[ndx2.keys, ax3].lebs ⊆ dom gstore2, ndx1.keys.toSet ⊆ dom fi2, fi2.lebs ⊆ dom gstore2, ndx2.keys.toSet ⊆ dom fi2, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ [abort; gstore := gstore3; index_set_gblock_refsize#(m3, n - m5, fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)], fi1, jro0, gstore1, nx, pmaxino, p_os, jvalid0; gstore3); index_get_gblock_refsize#(m, fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)], fi1, jro0, gstore3, gstore1, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(m, n + m1, fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)], fi1, jro0, gstore1, nx, pmaxino, p_os, jvalid0; gstore3); jmaxino := max(nd.key.ino + 1, jmaxino)] ( fi2[ndx2.keys, ax3].inos < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi2[ndx2.keys, ax3].inos ∪ (nd.key.inode? ⊃ ∅ ++ nd.key.ino;∅) < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0)) ∧ fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)].lebs ⊆ dom gstore3 ∧ refsize-cons(gstore3, range fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)]) ∧ inv(gstore3 \ jro0) ∧ dom gstore1 ∪ elems nx = dom gstore3 ∪ jro0 ∧ ri-inj(fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)]) ∧ gstore3 =○refsize gstore → ⟪ax0 := ax2; ndx0 := ndx1⟫ ( (∃ ax, ndx. # ax = # ndx ∧ ax3 + @(m, m0, m1) ' + ax2 = ax + ax0 ∧ ndx2 + nd ' + ndx1 = ndx + ndx0 ∧ fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)] = fi2[ndx.keys, ax]) ∧ (dom fi2 ∪ ndx2.keys.toSet) ++ nd.key = dom fi2 ∧ jmaxino1 ≤ jmaxino ∧ dom gstore3 = dom gstore2 ∧ nodes-cons(ax0, ndx0, gstore3, jro0) ∧ nodes(gstore ↓, jro0) = nodes(gstore2 ↓, jro0) ∧ abs-log(nx, gstore ↓) = abs-log(nx, gstore2 ↓) ∧ (jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0)) ∧ ¬ # ax2 < # ax0)), jmaxino = 0, jmaxino1 = 0, pmaxino = 0, dups(nx), dups(ax3 + ax2), dups(ax3), dups(ax2), m ∈ jro0, @(m, m0, m1) ∈ fi2, @(m, m0, m1) ∈ ax2, @(m, m0, m1) ∈ ax3, lnum ∈ gstore0

Heuristic symbolic execution applied rule abort right

And closed the goal!

Rule argument

Additional information