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Proof step 14 from proof range-write-in (previous step)

key0 ∈ ri[key, adr], key ∈ ri, ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ ri[key, adr][key0] = adr, ri[key, adr][key0] ≠ ri[key] ∧ (∃ key1. key1 ∈ ri ∧ ri[key1] = ri[key, adr][key0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ key ≠ key0 → ri[key0, adr][key] = ri[key]
Proof step 16:
key ∈ ri, key0 ∈ ri[key, adr], ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ ri[key0] = adr, key0 = key, ri[key0] ≠ ri[key] ∧ (∃ key1. key1 ∈ ri ∧ ri[key1] = ri[key0])

Rule argument

spec: store, inst: node-index name: At-other seq: ⊦ key ≠ key0 → ri[key0, adr][key] = ri[key] subst: [key, adr, key0, ri] → [key0, adr, key, ri] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ri[key, adr][key] = adr; (s) Used terms: key0, adr, key, ri