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Proof step 3 from proof restrict-le3 (previous step)

⊦ ri |≤ key0 |≤ key1 = ri |≤ key1, key0 < key1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ri = ri0 ↔ (∀ key. (key ∈ ri ↔ key ∈ ri0) ∧ (key ∈ ri → ri[key] = ri0[key]))
Proof step 5:
⊦ key0 < key1, ∀ key. (key ∈ ri |≤ key0 |≤ key1 ↔ key ∈ ri |≤ key1) ∧ (key ∈ ri |≤ key0 |≤ key1 → (ri |≤ key0 |≤ key1)[key] = (ri |≤ key1)[key])

Rule argument

spec: store, inst: node-index name: k-Extension seq: ⊦ ri = ri0 ↔ (∀ key. (key ∈ ri ↔ key ∈ ri0) ∧ (key ∈ ri → ri[key] = ri0[key])) subst: [ri0, ri] → [ri |≤ key1, ri |≤ key0 |≤ key1] flags: <all paths>

Additional information

Used terms: ri |≤ key1, ri |≤ key0 |≤ key1