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Proof step 3 from proof inv-sync (previous step)

remove-refsize0(gstore0) = gstore0, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro, pmaxino ≠ 0, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore \ jro), inv(gstore0), refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi0), ri-inj(fi), ri-inj(fi0), pmaxino ≤ jmaxino, fi.lebs ⊆ dom gstore, fi0.lebs ⊆ dom gstore0, ¬ dups(nx), jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro) ⊦ ⟪gjournal_journal_sync#(fi, fi0, jro, gstore, gstore0, nx, pmaxino, p_os; jvalid0; err)⟫ true

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 4:
jvalid ↔ jvalid0, fi = fi1, fi0 = fi2, gstore = gstore1, gstore0 = gstore2, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, inv(gstore1), inv(gstore2 \ jro), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ ⟪index_sync#(fi0, fi, jro, gstore0, gstore, nx, pmaxino, p_os; ; jvalid, err)⟫ true, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: sync: ⊦ ;