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Proof step 2 from proof refine-gc (previous step)

p_os.keys = fo, jro.keys = ro, fi = ri, fi0 = fi1, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), fo.inodes?, ro.inodes?, fi0.inos < pmaxino, fi.inos < jmaxino, p_os < pmaxino, jro < jmaxino, inv-journal(nx, gstore, gstore0, jro0), log-cons(log, fs), refsize-cons(gstore0, range fi0), refsize-cons(gstore, range fi), ri-cons(ri, fs), ri-inj(fi0), ri-inj(fi), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino, fi0.lebs ⊆ dom gstore0, fi.lebs ⊆ dom gstore, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid → jvalid0 ⊦ ⟪gjournal_journal_gc#(jvalid2, fi0, gstore0, pmaxino, p_os; jvalid1, jmaxino0, jmaxino, fi, jro0, gstore, nx, jvalid0)⟫ ⟨aubifs_core_journal_gc#(fi1, ro, fo; ri, fs, log; jvalid)⟩ (jro.keys = ro ∧ p_os.keys = fo ∧ fi = ri ∧ fi0 = fi1 ∧ log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid0)), jmaxino = 0, pmaxino = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
fi = ri, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, jro.keys.inodes?, p_os.keys.inodes?, jro < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore \ jro0), inv(gstore0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), refsize-cons(gstore, range ri), refsize-cons(gstore0, range fi1), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, ¬ dups(nx), jvalid → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟪gjournal_journal_gc#(jvalid2, fi1, gstore0, pmaxino, p_os; jvalid1, jmaxino0, jmaxino, fi, jro0, gstore, nx, jvalid0)⟫ ⟨aubifs_core_journal_gc#(fi1, jro.keys, p_os.keys; ri, fs, log; jvalid)⟩ (fi = ri ∧ log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid0))

Rule argument

Additional information

Used simplifier rules: ⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)