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Proof step 3 from proof del-merge-dels (previous step)

key ∈ ks ⊦ # ks = 0, ks = ∅, (ri ⊖ key) ⊖ ks = ri ⊖ ks

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:
key ∈ ks ⊦ # ks = 0, ks = ∅, ∀ key0. (key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ ri ⊖ ks) ∧ (key0 ∈ (ri ⊖ key) ⊖ ks → ((ri ⊖ key) ⊖ ks)[key0] = (ri ⊖ ks)[key0])

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 ⊖ ks, (ri ⊖ key) ⊖ ks] flags: <all paths>

Additional information

Used terms: ri ⊖ ks, (ri ⊖ key) ⊖ ks