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Proof step 11 from proof keys-remove-leb (previous step)

ax.toSet = (range ri0 | n) ++ @(n, m0, m1), ri-cons(ri0[key, @(n, m0, m1)], fs) ⊦ key ∈ ri0, @(n, m0, m1) ∈ ax ∧ fs[@(n, m0, m1)].key = key

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0)
Proof step 13:
ri-cons(ri0[key, @(n, m0, m1)], fs), ∀ adr. adr ∈ ax.toSet ↔ adr ∈ (range ri0 | n) ++ @(n, m0, m1) ⊦ key ∈ ri0, @(n, m0, m1) ∈ ax ∧ fs[@(n, m0, m1)].key = key

Rule argument

spec: set-basic, inst: node-store name: Extension seq: ⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0) subst: [as0, as] → [(range ri0 | n) ++ @(n, m0, m1), ax.toSet] flags: <all paths>

Additional information

Used terms: (range ri0 | n) ++ @(n, m0, m1), ax.toSet