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Proof step 9 from proof refine-newino (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), jvalid → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ∃ n. ¬ inodekey(n) ∈ ri ∧ ¬ n ∈ p_os ∧ n ≠ 0 ∧ ⟨key := inodekey(n)⟩ ((jvalid → jvalid0) ∧ inodekey(jmaxino) = key)

User applied rule exists right

And obtained the following new goals

Proof step 10:
remove-refsize0(gstore0) = gstore0, 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), jvalid → jvalid0 ⊦ ¬ inodekey(jmaxino) ∈ ri ∧ ¬ jmaxino ∈ p_os ∧ jmaxino ≠ 0 ∧ ⟨key := inodekey(jmaxino)⟩ ((jvalid → jvalid0) ∧ inodekey(jmaxino) = key), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1 terms: jmaxino abort: F discard: T computed: F

Additional information

Used terms: jmaxino