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Proof step 5 from proof elems-log-subset-gstore-union-ginval (previous step)

ns ∪ elems nx = dom gstore ∪ ginval ⊦ ∀ n. n ∈ elems nx → n ∈ dom gstore ∪ ginval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
ns ∪ elems nx = dom gstore ∪ ginval, n ∈ nx ⊦ n ∈ gstore, n ∈ ginval

Rule argument

Additional information

Used simplifier rules: elems-def: ⊦ n ∈ elems nx ↔ n ∈ nx;%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]% ⊦ n ∈ dom gstore ↔ n ∈ gstore; (s)% ⊦ n ∈ ns ∪ ns0 ↔ ¬(¬ n ∈ ns ∧ ¬ n ∈ ns0); (ss)