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Proof step 6 from proof fwd-in-gstore0 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
n ∈ dom gstore ∪ ginval, n ∈ dom gstore0 ∪ elems nx, n ∈ gstore ⊦ #(dom gstore ∪ ginval) = 0, #(dom gstore0 ∪ elems nx) = 0, dom gstore ∪ ginval = ∅, dom gstore0 ∪ elems nx = ∅, n ∈ gstore0, n ∈ nx

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[nat-set]%ne-01: ⊦ n ∈ ns → ns ≠ ∅; (forward) from specification set-basic[nat-set]%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)