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Proof step 6 from proof elems-log-subset-gstore-union-ginval (previous step)

ns ∪ elems nx = dom gstore ∪ ginval, n ∈ nx ⊦ n ∈ gstore, n ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 8:
n ∈ nx, ∀ n. n ∈ ns ∪ elems nx ↔ n ∈ dom gstore ∪ ginval ⊦ n ∈ ginval, n ∈ gstore

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [dom gstore ∪ ginval, ns ∪ elems nx] flags: <all paths>

Additional information

Used terms: dom gstore ∪ ginval, ns ∪ elems nx