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Proof step 1 from proof dom-remove-refsize0-down (conclusion)

⊦ dom remove-refsize0(gstore ↓) = dom remove-refsize0(gstore)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 3:
⊦ ∀ n. n ∈ dom remove-refsize0(gstore ↓) ↔ n ∈ dom remove-refsize0(gstore)

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [dom remove-refsize0(gstore), dom remove-refsize0(gstore ↓)] flags: <all paths>

Additional information

Used terms: dom remove-refsize0(gstore), dom remove-refsize0(gstore ↓)