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Proof step 6 from proof restr-add-notin (previous step)

⊦ n0 ∈ (ns ++ n) \ dom gstore ↔ n0 = n ∨ n0 ∈ ns \ dom gstore, n ∈ gstore

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ n ∈ ns \ ns0 ↔ n ∈ ns ∧ ¬ n ∈ ns0
Proof step 8:
⊦ n0 ∈ ns ++ n ∧ ¬ n0 ∈ dom gstore ↔ n0 = n ∨ n0 ∈ ns \ dom gstore, n ∈ gstore

Rule argument

spec: set-union, inst: nat-set name: Difference seq: ⊦ n ∈ ns \ ns0 ↔ n ∈ ns ∧ ¬ n ∈ ns0 subst: [ns0, ns, n] → [dom gstore, ns ++ n, n0] flags: <all paths>

Additional information

Used terms: dom gstore, ns ++ n, n0