[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 157 from proof inv-gc-copy (previous step)

jvalid ↔ jvalid0, abs-log(nx1, gstore2 ↓) = [], dom gstore1 = dom gstore3 ∪ jro, fi = fi1, fi0 = fi2, gstore = gstore1, gstore0 = gstore3, ndx0 = ndx4, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0), nx = [], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, fi2.inos < jmaxino0, jro2 < jmaxino3, p_os < pmaxino, fi2.inos < jmaxino3, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), inv(gstore3 \ jro), key-cons(ndx4), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi2), ri-inj(fi1), jmaxino3 ≤ jmaxino0, pmaxino ≤ jmaxino3, pmaxino ≤ jmaxino0, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ndx4.keys.toSet ⊆ dom fi2, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), fi2.lebs ⊆ dom gstore3, dom gstore2 ⊆ dom gstore3, jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0) ⊦ ⟪ndx3 := ndx4; ndx := []; gjournal_split_nodes#(LEB_SIZE - 0; ndx4, ndx); nx := []; fi := fi2; if ndx = [] then err := EINVAL else {ax0 := []; gjournal_journal_addn#(ndx, jvalid2, fi, fi1, gstore1, pmaxino, p_os; ax0, jvalid1, jmaxino1, jro, gstore3, nx, jvalid0; err); if err = ESUCCESS then gjournal_gc_update_index#(jvalid1, fi1, jro, gstore1, nx, pmaxino, p_os, jvalid0; ax0, ndx, jmaxino0, fi, gstore3)}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (∃ ndx. ndx0 = ndx + ndx4) ∧ jmaxino3 ≤ jmaxino0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro)) ∧ fi.inos < jmaxino0 ∧ fi.lebs ⊆ dom gstore3 ∧ refsize-cons(gstore3, range fi) ∧ inv(gstore3 \ jro) ∧ elems nx ∩ jro = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore3 ∪ jro ∧ ri-inj(fi) ∧ ndx4.keys.toSet ⊆ dom fi ∧ range fi ⊆ dom nodes(gstore3 ↓, jro) ∧ dom gstore2 ⊆ dom gstore3 ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅ ∧ (∃ ndx, ndx1. ndx0 = ndx + ndx1 ∧ (err = ESUCCESS → ndx1 = ndx4) ∧ new(abs-log(nx, gstore3 ↓), nodes(gstore2 ↓, jro0)) ∧ ¬ dups(abs-log(nx, gstore3 ↓)) ∧ # abs-log(nx, gstore3 ↓) = # ndx ∧ fi = fi2[ndx.keys, abs-log(nx, gstore3 ↓)] ∧ nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[abs-log(nx, gstore3 ↓), ndx]) ∧ (err = ESUCCESS ⊃ # ndx4;0) < # ndx3), jmaxino3 = 0, ndx4 = [], pmaxino = 0, dups(nx1), dups(ndx4.keys)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

Additional information