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Theorem inv-gc-update-index

jro < jmaxino, p_os < pmaxino, pmaxino ≤ jmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, jmaxino ≠ 0, pmaxino ≠ 0, jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), fi.lebs ⊆ dom gstore, fi0.lebs ⊆ dom gstore0, refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi0), inv-journal(nx, gstore, gstore0, jro0), ri-inj(fi), ri-inj(fi0), ndx.keys.toSet ⊆ dom fi, # ax = # ndx, key-cons(ndx), ax.toSet ∩ range fi = ∅, ¬ dups(ax), nodes-cons(ax, ndx, gstore, jro0), fi1 = fi, ndx0 = ndx, ax0 = ax, gstore1 = gstore, jro1 = jro0, nx0 = nx, jmaxino0 = jmaxino ⊦ ⟪gjournal_gc_update_index#(jvalid, fi0, jro0, gstore0, nx, pmaxino, p_os, jvalid0; ax, ndx, jmaxino, fi, gstore)⟫ ( jro < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv-journal(nx, gstore, gstore0, jro0) ∧ ri-inj(fi) ∧ fi = fi1[ndx0.keys, ax0] ∧ dom gstore = dom gstore1 ∧ nodes(gstore ↓, jro0) = nodes(gstore1 ↓, jro1) ∧ abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) ∧ jmaxino0 ≤ jmaxino)

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