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

remove-refsize0(gstore0) = gstore0, dom remove-refsize0(gstore) ∩ jro0 = ∅, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, jro < jmaxino, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore \ jro0), 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, fi.lebs ⊆ dom remove-refsize0(gstore), ¬ dups(nx), jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟪gjournal_commit#(jmaxino, jro, fi; fi0, jro0, gstore, gstore0, nx, pmaxino, p_os, jvalid0; err)⟫ ( p_os < pmaxino ∧ pmaxino ≤ jmaxino ∧ fi0.inos < pmaxino ∧ 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(gstore \ jro0) ∧ inv(gstore0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro0 ∧ remove-refsize0(gstore0) = gstore0 ∧ ri-inj(fi0))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 4:
jvalid ↔ jvalid0, fi = fi2, fi0 = fi1, gstore = gstore1, gstore0 = gstore2, jro1 = jro, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom remove-refsize0(gstore2) ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, jro < jmaxino, inv(gstore1), inv(gstore2 \ jro0), 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, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟪if dom remove-refsize0(gstore0) ∩ jro0 = ∅ ∧ fi0.lebs ⊆ dom remove-refsize0(gstore0) then {index_sync#(fi0, fi, jro0, gstore0, gstore, nx, pmaxino, p_os; ; jvalid, err); if err = ESUCCESS then let jro = jro1 in index_commit#(jmaxino, fi0, jvalid; jro, jro0, gstore0, fi, gstore, nx, pmaxino, p_os; err)} else abort⟫ ( p_os < pmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < pmaxino ∧ pmaxino ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore0, jro0)) ∧ fi1.lebs ⊆ dom gstore0 ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore0, range fi1) ∧ refsize-cons(gstore, range fi) ∧ inv(gstore0 \ jro0) ∧ inv(gstore) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore ∪ elems nx = dom gstore0 ∪ jro0 ∧ remove-refsize0(gstore) = gstore ∧ ri-inj(fi)), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: commit: ⊦ ;