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Proof step 3 from proof jnlhd-notin-ginval (previous step)

elems nx ∩ ginval = ∅, nx.last ∈ ginval ⊦ # ginval = 0, ginval = ∅, nx = []

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:
nx.last ∈ ginval, ∀ n. n ∈ elems nx ∩ ginval ↔ n ∈ ∅ ⊦ # ginval = 0, ginval = ∅, nx = []

Rule argument

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

Additional information

Used terms: ∅, elems nx ∩ ginval