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Proof step 32 from proof refine-gc (previous step)

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), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid5 → jvalid4 ⊦ ¬ dups([]) ∧ ¬ dups([]) ∧ new([], nodes(gstore2 ↓, jro0)) ∧ [].toSet ⊆ dom ri ∧ # [] = # [] ∧ [].toSet ∩ abs-log(nx, gstore2 ↓).toSet = ∅ ∧ ⟨fs := nodes(gstore2 ↓, jro0)[[], nodes(gstore2 ↓, jro0)[ri[[]]]], log := abs-log(nx, gstore2 ↓) + []; ri0 := ri[[], []]; aubifs_core_gc_drop#(ri0, log; fs); jvalid := ?⟩ (ri = ri0 ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro0) ∧ (jvalid → jvalid4)), jmaxino = 0, pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
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), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, ¬ dups(nx), jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟨fs := nodes(gstore2 ↓, jro0), log := abs-log(nx, gstore2 ↓); ri0 := ri; aubifs_core_gc_drop#(ri0, log; fs); jvalid := ?⟩ (ri = ri0 ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro0) ∧ (jvalid → jvalid4))

Rule argument

Additional information

Used simplifier rules: ⊦ ri[[], []] = ri; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + [] = ax; (s)% ⊦ fs[[], []] = fs; (s)% ⊦ fs[[]] = []; (s)% ⊦ ri[[]] = []; (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)% ⊦ [].toSet = ∅; (s)% ⊦ # [] = 0; (s)% ⊦ # [] = 0; (s)% ⊦ ∅ ⊆ ks; (s)% ⊦ [].toSet = ∅; (s)% ⊦ new([], fs); (s)% ⊦ ¬ dups([]); (s)% ⊦ ¬ dups([]); (s)