[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 14 from proof inv-check-commit (previous step)

remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom remove-refsize0(gstore2) ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, jmaxino ≠ 0, pmaxino ≠ 0, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, jro2 < jmaxino, inv(gstore1), inv(gstore2 \ jro), refsize-cons(gstore1, range fi2), refsize-cons(gstore2, range fi1), ri-inj(fi2), ri-inj(fi1), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom remove-refsize0(gstore2), fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore2, ¬ dups(nx), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪index_sync#(fi1, fi2, jro, gstore2, gstore1, nx, pmaxino, p_os; ; jvalid, err); if err = ESUCCESS then let jro1 = jro2 in index_commit#(jmaxino, fi1, jvalid; jro1, jro, gstore2, fi2, gstore1, nx, pmaxino, p_os; err)⟫ ( p_os < pmaxino ∧ pmaxino ≤ jmaxino ∧ fi2.inos < pmaxino ∧ pmaxino ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ fi1.lebs ⊆ dom gstore2 ∧ fi2.lebs ⊆ dom gstore1 ∧ refsize-cons(gstore2, range fi1) ∧ refsize-cons(gstore1, range fi2) ∧ inv(gstore2 \ jro) ∧ inv(gstore1) ∧ elems nx ∩ jro = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro ∧ remove-refsize0(gstore1) = gstore1 ∧ ri-inj(fi2))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 15:
fi = fi2, fi0 = fi1, gstore = gstore1, gstore0 = gstore2, remove-refsize0(gstore1) = gstore1, dom remove-refsize0(gstore2) ∩ jro = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, jro2 < jmaxino, p_os < pmaxino, fi1.inos < jmaxino, fi2.inos < pmaxino, inv(gstore2 \ jro), inv(gstore1), refsize-cons(gstore2, range fi1), refsize-cons(gstore1, range fi2), ri-inj(fi1), ri-inj(fi2), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom remove-refsize0(gstore2), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪fail_or_success#(; ; err); if err = ESUCCESS then jvalid := true else jvalid := ?; if err = ESUCCESS then let jro1 = jro2 in index_commit#(jmaxino, fi1, jvalid; jro1, jro, gstore2, fi2, gstore1, nx, pmaxino, p_os; err)⟫ ( p_os < pmaxino ∧ pmaxino ≤ jmaxino ∧ fi2.inos < pmaxino ∧ pmaxino ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro)) ∧ fi1.lebs ⊆ dom gstore2 ∧ fi2.lebs ⊆ dom gstore1 ∧ refsize-cons(gstore2, range fi1) ∧ refsize-cons(gstore1, range fi2) ∧ inv(gstore2 \ jro) ∧ inv(gstore1) ∧ elems nx ∩ jro = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro ∧ remove-refsize0(gstore1) = gstore1 ∧ ri-inj(fi2)), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: index_sync# (PRI, PFI, PINVAL, PSTORE, PSTORE0, PNL, PMAXINO, P_OS; ; ISYNCED, ERR ) {fail_or_success#(; ; ERR); if ERR = ESUCCESS then ISYNCED := true else ISYNCED := ? };