[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 4 from proof fwd-inv-loghead (previous step)

ginval ∩ elems nx = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, inv(gstore \ ginval) ⊦ inv(gstore[nx.last]), ∀ nx0, n. nx ≠ nx0 + n '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
(elems nx0 ∪ dom gstore0) ++ n = dom gstore ∪ ginval, ginval ∩ elems nx0 = ∅, inv(gstore \ ginval) ⊦ inv(gstore[n]), n ∈ ginval

Rule argument

Additional information

Used simplifier rules: elems-append: ⊦ elems(nx0 + n ') = elems nx0 ++ n;% ⊦ (nx + n ').last = n; (s)%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ ns ∩ (ns0 ++ n) = ∅ ↔ ns ∩ ns0 = ∅ ∧ ¬ n ∈ ns; (ws)%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]% ⊦ (ns ++ n) ∪ ns0 = (ns ∪ ns0) ++ n; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]