[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 405 from proof refine-gc (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 406:
gstore2[n1] = groupblock(gndx, lax, 0), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = jro0 ∪ dom gstore2, #(jro0 ∪ dom gstore2) ≠ 0, jmaxino ≠ 0, pmaxino ≠ 0, jro0 ∪ dom gstore2 ≠ ∅, p_os.keys.inodes?, jro1.keys.inodes?, ri.inos < jmaxino, jro1 < jmaxino, p_os < pmaxino, fi1.inos < pmaxino, inv(gstore1), inv(gstore2 \ jro0), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), refsize-cons(gstore2 -- n1, range ri), ri-cons(ri, nodes(gstore2 ↓, jro0)), ri-inj(ri), ri-inj(fi1), n1 ∈ jro0 ∪ dom gstore2, n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ¬ dups(nx), ¬ n1 ∈ nx, jvalid5 → jvalid0, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore2 -- n1, jro0 ++ n1) ⊦ (dom nodes(gstore2 ↓, jro0) | n1) ∩ range ri = ∅ ∧ ⟨fs := nodes(gstore2 ↓, jro0) \ (dom nodes(gstore2 ↓, jro0) | n1); jvalid := ?⟩ (fs = nodes(gstore2 ↓, jro0) \ (dom nodes(gstore2 ↓, jro0) | n1)), ∃ adr. adr.lnum = n1 ∧ adr ∈ ri

Rule argument

Additional information

Used simplifier rules: 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]% ⊦ ¬ n ∈ nx → abs-log(nx, gstore).toSet ∩ (as | n) = ∅; (s)