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Proof step 5 from proof notin-gstore-ginval-notin-gstore0 (previous step)

n ∈ gstore0, ∀ n. n ∈ dom gstore0 ∪ elems nx ↔ n ∈ dom gstore ∪ ginval ⊦ n ∈ ginval, n ∈ gstore

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: n

Additional information

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