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Proof step 7 from proof refine-orphans-insert (previous step)

jro.keys = ro, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, key.inode?, 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-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, jvalid → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟨aubifs_core_orphans_insert#(key, ri, fi1, p_os.keys, nodes(gstore ↓, jro0), abs-log(nx, gstore ↓), jvalid; ro)⟩ ((jro ++ key.ino).keys = ro ∧ (jvalid → jvalid0)), jmaxino = 0, pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
jro.keys = ro, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, key.inode?, p_os.keys.inodes?, jro.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro < jmaxino, inv(gstore0), inv(gstore \ jro0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range ri), 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 ⊦ ⟨aubifs_core_orphans_insert#(key, ri, fi1, p_os.keys, nodes(gstore ↓, jro0), abs-log(nx, gstore ↓), jvalid; ro)⟩ (jro.keys ++ key = ro ∧ (jvalid → jvalid0))

Rule argument

Additional information

Used simplifier rules: ⊦ key.inode? → inodekey(key.ino) = key; (s)% ⊦ (ns ++ n).keys = ns.keys ++ inodekey(n); (s)