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Proof step 189 from proof refine-gc (previous step)

# lax = # gndx0, # ax0 = # referenced-adrs(lax.to-adr(n1), ri), gstore2[n1] = groupblock(gndx0, lax, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax0, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax0, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)]], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro = ∅, dom gstore1 ∪ elems nx0 = jro ∪ dom gstore3, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0].inos < jmaxino0, jro1 < jmaxino0, inv(gstore2 \ jro0), inv(gstore1), inv(groupblock(gndx0, lax, m0)), inv(gstore3 \ jro), log-cons(abs-log(nx1, gstore2 ↓), nodes(gstore2 ↓, jro0)), new(ax0, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3 -- n1, range ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0]), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), refsize-cons(gstore3, range ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0]), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(fi1), ri-inj(ri), ri-inj(ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0]), n1 ∈ jro ∪ dom gstore3, n1 ∈ gstore3, n1 ∈ gstore2, n1 ∈ gstore1, pmaxino ≤ jmaxino, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino0, range ri ⊆ dom nodes(gstore2 ↓, jro0), fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, dom gstore2 ⊆ dom gstore3, ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0].lebs ⊆ dom gstore3, ri.lebs ⊆ dom gstore3, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3 -- n1, jro ++ n1), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid3 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid5 → jvalid4 ⊦ ¬ dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys) ∧ ¬ dups(ax0) ∧ new(ax0, nodes(gstore2 ↓, jro0)) ∧ nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys.toSet ⊆ dom ri ∧ # nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys = # ax0 ∧ ax0.toSet ∩ abs-log(nx1, gstore2 ↓).toSet = ∅ ∧ ⟨fs := nodes(gstore2 ↓, jro0)[ax0, nodes(gstore2 ↓, jro0)[ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys]]], log := abs-log(nx1, gstore2 ↓) + ax0; ri1 := ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0]; aubifs_core_gc_drop#(ri1, log; fs); jvalid := ?⟩ ( ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0] = ri1 ∧ log = abs-log(nx0, gstore3 ↓) ∧ fs = nodes(gstore3 ↓, jro) \ (dom nodes(gstore3 ↓, jro) | n1)), #(jro ∪ dom gstore3) = 0, jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, jro ∪ dom gstore3 = ∅, dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys), dups(nx1), dups(nx0), dups(ax0), n1 ∈ nx1, n1 ∈ jro0, n1 ∈ nx0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 190:
# ax0 = # referenced-adrs(lax.to-adr(n1), ri), # lax = # gndx0, gstore2[n1] = groupblock(gndx0, lax, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax0, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax0, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)]], remove-refsize0(gstore1) = gstore1, elems nx0 ∩ jro = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx0 = jro ∪ dom gstore3, #(jro ∪ dom gstore3) ≠ 0, jmaxino ≠ 0, jmaxino0 ≠ 0, m0 ≠ 0, pmaxino ≠ 0, jro ∪ dom gstore3 ≠ ∅, p_os.keys.inodes?, jro1.keys.inodes?, jro1 < jmaxino0, ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0].inos < jmaxino0, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore3 \ jro), inv(groupblock(gndx0, lax, m0)), inv(gstore1), inv(gstore2 \ jro0), log-cons(abs-log(nx1, gstore2 ↓), nodes(gstore2 ↓, jro0)), new(ax0, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3, range ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0]), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), refsize-cons(gstore3 -- n1, range ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0]), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0]), ri-inj(ri), ri-inj(fi1), n1 ∈ gstore1, n1 ∈ gstore2, n1 ∈ gstore3, n1 ∈ jro ∪ dom gstore3, pmaxino ≤ jmaxino0, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore3, ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0].lebs ⊆ dom gstore3, dom gstore2 ⊆ dom gstore3, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, range ri ⊆ dom nodes(gstore2 ↓, jro0), ¬ dups(ax0), ¬ dups(nx0), ¬ dups(nx1), ¬ dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys), ¬ n1 ∈ nx0, ¬ n1 ∈ jro0, ¬ n1 ∈ nx1, jvalid5 → jvalid4, jvalid3 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3 -- n1, jro ++ n1) ⊦ ax0.toSet ∩ abs-log(nx1, gstore2 ↓).toSet = ∅ ∧ ⟨fs := nodes(gstore3 ↓, jro), log := abs-log(nx0, gstore3 ↓); ri1 := ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0]; aubifs_core_gc_drop#(ri1, log; fs); jvalid := ?⟩ ( ri[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys, ax0] = ri1 ∧ log = abs-log(nx0, gstore3 ↓) ∧ fs = nodes(gstore3 ↓, jro) \ (dom nodes(gstore3 ↓, jro) | n1))

Rule argument

Additional information

Used simplifier rules: ⊦ ri-cons(ri, fs) → ri[fs[referenced-adrs(ax, ri)].keys] = referenced-adrs(ax, ri); (s)% ⊦ # fs[ax] = # ax; (s)% ⊦ # ndx.keys = # ndx; (s)% ⊦ ri-cons(ri, fs) → fs[referenced-adrs(ax, ri)].keys.toSet ⊆ dom ri; (s)