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Proof step 22 from proof replay-nonorphans-trunc (previous step)

key0 ∈ ri ⊦ ((ri ⊖ ro) \ datakeys(key, n, ri))[key0] = (ri \ datakeys(key, n, ri))[key0], key0.data?, key0 ∈ ro, key ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: node-index name: Diff-get seq: ⊦ ¬ key ∈ ks → (ri \ ks)[key] = ri[key] subst: [key, ks, ri] → [key0, datakeys(key, n, ri), ri ⊖ ro] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key]; (s)% ⊦ ¬ key ∈ ks → (ri \ ks)[key] = ri[key]; (s)% ⊦ key ∈ ks → (ri \ ks)[key] = (∅)[key]; (s) Used terms: key0, datakeys(key, n, ri), ri ⊖ ro