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Proof step 2 from proof prefix-imp-dom-nodes-subset (previous step)

st0 ⊑ st ⊦ dom nodes(st0) ⊆ dom nodes(st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ as ⊆ as0 ↔ (∀ adr. adr ∈ as → adr ∈ as0)

Rule argument

spec: set-basic, inst: address-store name: Subset seq: ⊦ as ⊆ as0 ↔ (∀ adr. adr ∈ as → adr ∈ as0) subst: [as0, as] → [dom nodes(st), dom nodes(st0)] flags: <all paths>

Additional information

Used simplifier rules: in-nodes: ⊦ adr ∈ nodes(st) ↔ adr ∈ st;% ⊦ adr ∈ dom ast ↔ adr ∈ ast; (s)%prefix-at: ⊦ adr ∈ st0 ∧ st0 ⊑ st1 → st0[adr] = st1[adr]; (forward) from specification ablock-store-inv%prefix-in: ⊦ adr ∈ st0 ∧ st0 ⊑ st1 → adr ∈ st1; (forward) from specification ablock-store-inv%prefix-notin-fwd: ⊦ ¬ adr ∈ st1 ∧ st0 ⊑ st1 → ¬ adr ∈ st0; (forward) from specification ablock-store-inv Used terms: dom nodes(st), dom nodes(st0)