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Proof step 19 from proof prefix-subseteq-dom-nodes-rev (previous step)

@(m, m0, m1) ∈ st0, ∀ n. n ∈ st0 ∧ n ∈ st1 → st0[n].list ⊑ st1[n].list ∧ st0[n].ladrlist ⊑ st1[n].ladrlist ∧ # st0[n].list = # st0[n].ladrlist ∧ # st1[n].list = # st1[n].ladrlist, ∀ n. n ∈ st0 → n ∈ st1 ⊦ @(m, m0, m1) ∈ st1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ adr ∈ st ↔ adr.lnum ∈ st ∧ @(adr.pos, adr.size) ∈ st[adr.lnum].ladrlist
Proof step 21:
@(m, m0, m1).lnum ∈ st0, @(@(m, m0, m1).pos, @(m, m0, m1).size) ∈ st0[@(m, m0, m1).lnum].ladrlist, ∀ n. n ∈ st0 → n ∈ st1, ∀ n. n ∈ st0 ∧ n ∈ st1 → st0[n].list ⊑ st1[n].list ∧ st0[n].ladrlist ⊑ st1[n].ladrlist ∧ # st0[n].list = # st0[n].ladrlist ∧ # st1[n].list = # st1[n].ladrlist ⊦ @(m, m0, m1) ∈ st1

Rule argument

spec: ablock-store-inv name: in seq: ⊦ adr ∈ st ↔ adr.lnum ∈ st ∧ @(adr.pos, adr.size) ∈ st[adr.lnum].ladrlist subst: [st, adr] → [st0, @(m, m0, m1)] flags: <all paths>

Additional information

Used terms: st0, @(m, m0, m1)