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Proof step 9 from proof fwd-inv-loghead (previous step)

(elems nx0 ∪ dom gstore0) ++ n = dom gstore ∪ ginval, ginval ∩ elems nx0 = ∅ ⊦ inv((∅)[n]), n ∈ gstore, n ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 11:
ginval ∩ elems nx0 = ∅, ∀ n0. n0 ∈ (elems nx0 ∪ dom gstore0) ++ n ↔ n0 ∈ dom gstore ∪ ginval ⊦ inv((∅)[n]), 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, (elems nx0 ∪ dom gstore0) ++ n] flags: <all paths>

Additional information

Used terms: dom gstore ∪ ginval, (elems nx0 ∪ dom gstore0) ++ n