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Proof step 3 from proof prefix-rem (previous step)

dom st0 \ ns ⊆ dom st \ ns, ∀ n. n ∈ st0 \ ns ∧ n ∈ st \ ns → (st0 \ ns)[n].list ⊑ (st \ ns)[n].list ∧ (st0 \ ns)[n].ladrlist ⊑ (st \ ns)[n].ladrlist ∧ # (st0 \ ns)[n].list = # (st0 \ ns)[n].ladrlist ∧ # (st \ ns)[n].list = # (st \ ns)[n].ladrlist ⊦ (st0 \ ns) -- n ⊑ (st \ ns) -- n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ st0 ⊑ st ↔ dom st0 ⊆ dom st ∧ (∀ n. n ∈ st0 ∧ n ∈ st → st0[n].list ⊑ st[n].list ∧ st0[n].ladrlist ⊑ st[n].ladrlist ∧ # st0[n].list = # st0[n].ladrlist ∧ # st[n].list = # st[n].ladrlist)
Proof step 5:
dom st0 \ ns ⊆ dom st \ ns, ∀ n. n ∈ st0 \ ns ∧ n ∈ st \ ns → (st0 \ ns)[n].list ⊑ (st \ ns)[n].list ∧ (st0 \ ns)[n].ladrlist ⊑ (st \ ns)[n].ladrlist ∧ # (st0 \ ns)[n].list = # (st0 \ ns)[n].ladrlist ∧ # (st \ ns)[n].list = # (st \ ns)[n].ladrlist ⊦ dom((st0 \ ns) -- n) ⊆ dom((st \ ns) -- n) ∧ (∀ n0. n0 ∈ (st0 \ ns) -- n ∧ n0 ∈ (st \ ns) -- n → ((st0 \ ns) -- n)[n0].list ⊑ ((st \ ns) -- n)[n0].list ∧ ((st0 \ ns) -- n)[n0].ladrlist ⊑ ((st \ ns) -- n)[n0].ladrlist ∧ # ((st0 \ ns) -- n)[n0].list = # ((st0 \ ns) -- n)[n0].ladrlist ∧ # ((st \ ns) -- n)[n0].list = # ((st \ ns) -- n)[n0].ladrlist)

Rule argument

spec: <toplevel> name: blockstore-prefix seq: ⊦ st0 ⊑ st ↔ dom st0 ⊆ dom st ∧ (∀ n. n ∈ st0 ∧ n ∈ st → st0[n].list ⊑ st[n].list ∧ st0[n].ladrlist ⊑ st[n].ladrlist ∧ # st0[n].list = # st0[n].ladrlist ∧ # st[n].list = # st[n].ladrlist) subst: [st, st0] → [(st \ ns) -- n, (st0 \ ns) -- n] flags: <all paths>

Additional information

Used terms: (st \ ns) -- n, (st0 \ ns) -- n