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Proof step 7 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, 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), jvalid4 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟨aubifs_core_orphans_contains#(key, ri, fi1, jro.keys, p_os.keys, nodes(gstore ↓, jro0), abs-log(nx, gstore ↓), jvalid4; jvalid3)⟩ ((jvalid4 → jvalid0) ∧ (key.ino ∈ jro ↔ jvalid3))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
key = inodekey(m), 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 ⊦ ⟨aubifs_core_orphans_contains#(key, ri, fi1, jro.keys, p_os.keys, nodes(gstore ↓, jro0), abs-log(nx, gstore ↓), jvalid4; jvalid3)⟩ ((jvalid4 → jvalid0) ∧ (m ∈ jro ↔ jvalid3)), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

spec: key name: elim-01 seq: ⊦ key.inode? → (m = key.ino ↔ key = inodekey(m)) subst: [key, m] → [key, m]

Additional information

Used simplifier rules: ⊦ key.inode? → (m = key.ino ↔ key = inodekey(m)); (elim) Used terms: key, m