[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 241 from proof refine-gc (previous step)

# 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, fs = nodes(gstore2 ↓, jro0), log = abs-log(nx1, gstore2 ↓), nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax0, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)]], remove-refsize0(gstore1) = gstore1, ri0 = ri, elems nx0 ∩ jro = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, 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), 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, 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), ⌊err0⌋ , jvalid5 → jvalid4, jvalid3 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro) ⊦ ∃ kx, ax. (¬ dups(kx) ∧ ¬ dups(ax) ∧ new(ax, fs) ∧ kx.toSet ⊆ dom ri ∧ # kx = # ax ∧ ax.toSet ∩ log.toSet = ∅) ∧ ⟨fs[ax] := fs[ri[kx]], log := log + ax; ri[kx] := ax; aubifs_core_gc_drop#(ri, log; fs); jvalid := ?⟩ ( ri0[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri0)].keys, ax0] = ri ∧ log = abs-log(nx0, gstore3 ↓) ∧ fs = nodes(gstore3 ↓, jro)), jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, 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 242:
# 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 nx1 = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro, jmaxino ≠ 0, jmaxino0 ≠ 0, m0 ≠ 0, pmaxino ≠ 0, 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(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 ∈ 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, ⌊err0⌋ , ¬ dups(ax0), ¬ dups(nx0), ¬ dups(nx1), ¬ dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), ri)].keys), ¬ n1 ∈ nx0, ¬ n1 ∈ jro0, ¬ n1 ∈ nx1, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid3 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid5 → jvalid4 ⊦ ∃ kx, ax. ¬ dups(kx) ∧ ¬ dups(ax) ∧ new(ax, nodes(gstore2 ↓, jro0)) ∧ kx.toSet ⊆ dom ri ∧ # kx = # ax ∧ ax.toSet ∩ abs-log(nx1, gstore2 ↓).toSet = ∅ ∧ ⟨fs := nodes(gstore2 ↓, jro0)[ax, nodes(gstore2 ↓, jro0)[ri[kx]]], log := abs-log(nx1, gstore2 ↓) + ax; ri1 := ri[kx, ax]; 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))

Proof step 241 from proof refine-gc (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information