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Proof step 7 from proof fwd-in-gstore0 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 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 nx, dom gstore0, n] flags: <all paths>

Additional information

Used simplifier rules: elems-def: ⊦ n ∈ elems nx ↔ n ∈ nx;% ⊦ n ∈ dom gstore ↔ n ∈ gstore; (s) Used terms: elems nx, dom gstore0, n