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Proof step 8 from proof range-write-in (previous step)

key ∈ ri, ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ adr0 ∈ ri[key, adr] ↔ adr0 = adr ∨ adr0 ≠ ri[key] ∧ adr0 ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 10:
key ∈ ri, ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ (∃ key0. key0 ∈ ri[key, adr] ∧ ri[key, adr][key0] = adr0) ↔ adr0 = adr ∨ adr0 ≠ ri[key] ∧ adr0 ∈ ri

Rule argument

spec: store+set, inst: node-index name: Data-in seq: ⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr) subst: [ri, adr] → [ri[key, adr], adr0] flags: <all paths>

Additional information

Used terms: ri[key, adr], adr0