[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 42 from proof inv-recover (previous step)

remove-refsize0(gstore3) = gstore3, elems nx3 ∩ jro3 = ∅, fi4.inos < jmaxino0, fi1.inos < jmaxino3, jro5 < jmaxino0, jro2 < jmaxino3, inv(gstore3), inv(gstore2 \ jro3), refsize-cons(gstore3, range fi4), refsize-cons(gstore2, range fi1), ri-inj(fi4), ri-inj(fi1), n ∈ dom gstore2 ∪ jro3, n ∈ dom gstore3 ∪ elems nx3, n ∈ jro3, jmaxino0 ≤ jmaxino3, fi4.lebs ⊆ dom gstore3, fi1.lebs ⊆ dom gstore2, jvalid0 ∧ nx3 ≠ [] → valid-journal-head(nx3, gstore2, jro3) ⊦ # jro3 = 0, #(dom gstore2 ∪ jro3) = 0, #(dom gstore3 ∪ elems nx3) = 0, jmaxino0 = 0, jmaxino3 = 0, jro3 = ∅, dom gstore2 ∪ jro3 = ∅, dom gstore3 ∪ elems nx3 = ∅, dups(nx3), inv(gstore3[n]), n ∈ nx3

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ n ∈ ns ∪ ns0 ↔ n ∈ ns ∨ n ∈ ns0

Rule argument

spec: set-union, inst: nat-set name: Union seq: ⊦ n ∈ ns ∪ ns0 ↔ n ∈ ns ∨ n ∈ ns0 subst: [ns0, ns, n] → [elems nx3, dom gstore3, n] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ dom gstore ↔ n ∈ gstore; (s)% ⊦ n ∈ elems nx ↔ n ∈ nx; (s)% ⊦ n ∈ gstore ∧ inv(gstore) → (inv(gstore[n]) ↔ true); (ss) Used terms: elems nx3, dom gstore3, n