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Proof step 2 from proof refine-add2 (previous step)

p_os.keys = fo, jro.keys = ro, adr = adr0, adr1 = adr2, 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), node-cons(nd0.key, nd0), node-cons(nd.key, nd), 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_add2#(nd, nd0, jvalid2, fi, fi0, gstore0, pmaxino, p_os; adr, adr1, jvalid1, jmaxino0, jro0, gstore, nx, jvalid0; err)⟫ ⟨aubifs_core_journal_add2#(nd, nd0, ri, fi1, ro, fo; adr0, adr2, fs, log; jvalid, err0)⟩ ( (jro.keys = ro ∧ p_os.keys = fo ∧ fi = ri ∧ fi0 = fi1 ∧ log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid0)) ∧ adr = adr0 ∧ adr1 = adr2 ∧ err = err0), jmaxino = 0, pmaxino = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
adr = adr0, adr1 = adr2, 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)), node-cons(nd.key, nd), node-cons(nd0.key, nd0), 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_add2#(nd, nd0, jvalid2, ri, fi1, gstore0, pmaxino, p_os; adr, adr1, jvalid1, jmaxino0, jro0, gstore, nx, jvalid0; err)⟫ ⟨aubifs_core_journal_add2#(nd, nd0, ri, fi1, jro.keys, p_os.keys; adr0, adr2, fs, log; jvalid, err0)⟩ (log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid0) ∧ adr = adr0 ∧ adr1 = adr2 ∧ err = err0)

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)