[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 47 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), gstore3[m3] = groupblock(gndx, lax, m6), 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 = gstore3, gstore0 = gstore1, gstore4 = gstore3, jro = jro0, lnum = m3, n = m6 - m5, 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), m3 ∈ gstore3, nd.key ∈ fi2[ndx2.keys, ax3], @(m, m0, m1) ∈ gstore3, nd.key ∈ fi2, m3 ∈ gstore2, pmaxino ≤ jmaxino, pmaxino ≤ jmaxino1, jmaxino1 ≤ jmaxino, m6 ≥ m5, 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) ⊦ [if lnum ∈ gstore then gstore[lnum].ref-size := n else abort; index_get_gblock_refsize#(m, fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)], fi1, jro0, gstore, 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; gstore); 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, gstore, jro0)) ∧ fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)].lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)]) ∧ inv(gstore \ jro0) ∧ dom gstore1 ∪ elems nx = dom gstore ∪ jro0 ∧ ri-inj(fi2[ndx2.keys, ax3][nd.key, @(m, m0, m1)]) ∧ gstore =○refsize gstore4 → ⟪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 gstore = dom gstore2 ∧ nodes-cons(ax0, ndx0, gstore, jro0) ∧ nodes(gstore4 ↓, jro0) = nodes(gstore2 ↓, jro0) ∧ abs-log(nx, gstore4 ↓) = abs-log(nx, gstore2 ↓) ∧ (jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore, 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

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Rule argument

Additional information