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Proof step 3 from proof fwd-in-gstore0 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 5:
n ∈ gstore, ∀ n. n ∈ dom gstore0 ∪ elems nx ↔ n ∈ dom gstore ∪ ginval ⊦ n ∈ gstore0, n ∈ nx

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [dom gstore ∪ ginval, dom gstore0 ∪ elems nx] flags: <all paths>

Additional information

Used terms: dom gstore ∪ ginval, dom gstore0 ∪ elems nx