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Proof step 3 from proof remove-refsize0-refsize-cons (previous step)

inv(st), as ⊆ dom nodes(st), ∀ n. n ∈ st → st[n].ref-size = (as | n).size ⊦ as ⊆ dom nodes(remove-refsize0(st)), dom nodes(st) ⊆ dom nodes(remove-refsize0(st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ as ⊆ as0 ↔ (∀ adr. adr ∈ as → adr ∈ as0)
Proof step 5:
inv(st), as ⊆ dom nodes(st), ∀ n. n ∈ st → st[n].ref-size = (as | n).size ⊦ dom nodes(st) ⊆ dom nodes(remove-refsize0(st)), ∀ adr. adr ∈ as → adr ∈ dom nodes(remove-refsize0(st))

Rule argument

spec: set-basic, inst: address-store name: Subset seq: ⊦ as ⊆ as0 ↔ (∀ adr. adr ∈ as → adr ∈ as0) subst: [as0, as] → [dom nodes(remove-refsize0(st)), as] flags: <all paths>

Additional information

Used terms: dom nodes(remove-refsize0(st)), as