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Proof step 3 from proof refine-orphans-contains (previous step)

jvalid2 ↔ jvalid3, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, 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, ¬ dups(nx), jvalid → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟪gjournal_orphans_contains#(key, jro; jvalid2)⟫ ⟨aubifs_core_orphans_contains#(key, ri, fi1, jro.keys, p_os.keys, nodes(gstore ↓, jro0), abs-log(nx, gstore ↓), jvalid; jvalid3)⟩ ((jvalid → jvalid0) ∧ (jvalid2 ↔ jvalid3))

Heuristic weak unfold applied rule call right

And obtained the following new goals

Proof step 4:
jvalid ↔ jvalid2, jvalid2 ↔ jvalid3, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, 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, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid4 → jvalid0 ⊦ ⟪if key.inode? then jvalid := key.ino ∈ jro else abort⟫ ⟨aubifs_core_orphans_contains#(key, ri, fi1, jro.keys, p_os.keys, nodes(gstore ↓, jro0), abs-log(nx, gstore ↓), jvalid4; jvalid3)⟩ ((jvalid4 → jvalid0) ∧ (jvalid ↔ jvalid3)), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: gjournal_orphans_contains#(KEY, JRO; EXISTS) {if KEY.inode? then EXISTS := KEY.ino ∈ JRO else abort};