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Proof step 2 from proof elems-empty (previous step)

⊦ # elems [] = 0, elems [] = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)

Rule argument

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

Additional information

Used simplifier rules: elems-def: ⊦ n ∈ elems nx ↔ n ∈ nx;% ⊦ ¬ n ∈ []; (s)% ⊦ ¬ n ∈ ∅; (s) Used terms: ∅, elems []