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Proof step 82 from proof refine-lookup (previous step)

remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore1), inv(gstore2 \ jro0), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, ¬ dups(nx), ¬ key ∈ ri, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid4 → jvalid2 ⊦ ∃ err0. (⌊err0⌋ ∨ err0 = ESUCCESS) ∧ ⟨err := err0; if err = ESUCCESS then {jvalid := key ∈ ri; if jvalid then nd := nodes(gstore2 ↓, jro0)[ri[key]] else nd := ?} else jvalid := ?, nd := ?⟩ ((jvalid4 → jvalid2) ∧ ¬ jvalid ∧ nd0 = nd ∧ ESUCCESS = err)

User applied rule exists right

And obtained the following new goals

Proof step 83:
remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid4 → jvalid2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ (⌊ESUCCESS⌋ ∨ ESUCCESS = ESUCCESS) ∧ ⟨err := ESUCCESS; if err = ESUCCESS then {jvalid := key ∈ ri; if jvalid then nd := nodes(gstore2 ↓, jro0)[ri[key]] else nd := ?} else jvalid := ?, nd := ?⟩ ((jvalid4 → jvalid2) ∧ ¬ jvalid ∧ nd0 = nd ∧ ESUCCESS = err), jmaxino = 0, pmaxino = 0, dups(nx), key ∈ ri

Rule argument

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

Additional information

Used terms: ESUCCESS