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

⊦ dom remove-refsize0(st) ⊆ dom st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ns ⊆ ns0 ↔ (∀ n. n ∈ ns → n ∈ ns0)

Rule argument

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

Additional information

Used simplifier rules: in-remove-refsize0: ⊦ n ∈ remove-refsize0(st) ↔ n ∈ st ∧ st[n].ref-size ≠ 0;% ⊦ n ∈ dom st ↔ n ∈ st; (s)% ⊦ ¬ n ∈ st → st[n] = (∅)[n]; (s) Used terms: dom st, dom remove-refsize0(st)