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Proof step 459 from proof refine-gc (previous step)

gstore2[n1] = groupblock(gndx, lax, 0), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, ri.inos < jmaxino, fi1.inos < pmaxino, p_os < pmaxino, jro1 < jmaxino, 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), n1 ∈ gstore2, n1 ∈ gstore1, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ⌊err0⌋ , jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid5 → jvalid0 ⊦ ∅ ∩ range ri = ∅ ∧ abs-log(nx, gstore2 ↓).toSet ∩ ∅ = ∅ ∧ ⟨fs := nodes(gstore2 ↓, jro0) \ ∅; jvalid := ?⟩ (fs = nodes(gstore2 ↓, jro0) ∧ (jvalid → jvalid4)), jmaxino = 0, pmaxino = 0, dups(nx), n1 ∈ nx

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 460:
gstore2[n1] = groupblock(gndx, lax, 0), 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?, jro1 < jmaxino, p_os < pmaxino, fi1.inos < pmaxino, ri.inos < 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), n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, ⌊err0⌋ , ¬ dups(nx), ¬ n1 ∈ nx, jvalid5 → jvalid0, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟨fs := nodes(gstore2 ↓, jro0); jvalid := ?⟩ (fs = nodes(gstore2 ↓, jro0) ∧ (jvalid → jvalid4))

Rule argument

Additional information

Used simplifier rules: ⊦ fs \ ∅ = fs; (s)%int-c: ⊦ as ∩ as0 = as0 ∩ as; from specification set-union[node-store]%int-a: ⊦ (as ∩ as0) ∩ as1 = as ∩ as0 ∩ as1; from specification set-union[node-store]% ⊦ as ∩ ∅ = ∅; (s)