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Proof step 9 from proof refine-orphans-contains (previous step)

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-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, ¬ dups(nx), jvalid4 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟨aubifs_core_orphans_contains#(inodekey(m), ri, fi1, jro.keys, p_os.keys, nodes(gstore ↓, jro0), abs-log(nx, gstore ↓), jvalid4; jvalid3)⟩ ((jvalid4 → jvalid0) ∧ (m ∈ jro ↔ jvalid3))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 10:
jvalid0 ↔ jvalid4, jvalid ↔ jvalid3, fi = fi1, fo = p_os.keys, fs = nodes(gstore ↓, jro0), key = inodekey(m), log = abs-log(nx, gstore ↓), remove-refsize0(gstore0) = gstore0, ro = jro.keys, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, 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 → jvalid2 ⊦ ⟨if key.inode? then jvalid := key ∈ ro else abort⟩ ((jvalid4 → jvalid2) ∧ (m ∈ jro ↔ jvalid)), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_orphans_contains# (KEY, RI, FI, RO, FO, FS, LOG, CSYNCED; EXISTS) {if KEY.inode? then EXISTS := KEY ∈ RO else abort};