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Proof step 5 from proof refine-gc (previous step)

jvalid3 ↔ jvalid2, fi = ri, fi2 = fi1, fs = nodes(gstore ↓, jro0), gstore1 = gstore0, jro1 = jro, log = abs-log(nx, gstore ↓), p_os0 = p_os, pmaxino0 = pmaxino, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, p_os.keys.inodes?, jro.keys.inodes?, ri.inos < jmaxino, jro < jmaxino, p_os < pmaxino, fi.inos < jmaxino, fi1.inos < pmaxino, inv(gstore0), inv(gstore \ jro0), inv-journal(nx, gstore, gstore0, jro0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), refsize-cons(gstore, range ri), refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi1), ri-cons(ri, nodes(gstore ↓, jro0)), ri-cons(fi, nodes(gstore ↓, jro0)), ri-inj(ri), ri-inj(fi), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore, fi.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, 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)] ( jro1 < jmaxino ∧ pmaxino0 ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv-journal(nx, gstore, gstore1, jro0) ∧ ri-inj(fi) → ⟨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))), jmaxino = 0, pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
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?, fi1.inos < pmaxino, p_os < pmaxino, jro < jmaxino, ri.inos < jmaxino, inv(gstore \ jro0), inv(gstore0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range ri), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore0, ri.lebs ⊆ dom gstore, ¬ dups(nx), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid → jvalid0 ⊦ [gjournal_journal_gc#(jvalid2, fi1, gstore0, pmaxino, p_os; jvalid1, jmaxino0, jmaxino, fi, jro0, gstore, nx, jvalid0)] ( jro < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv(gstore \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro0 ∧ ri-inj(fi) → ⟨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)