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Proof step 25 from proof replay-nonorphans-trunc (previous step)

⊦ key0 ∈ (ri ⊖ ro) \ datakeys(key, n, ri) ↔ key0 ∈ (ri \ datakeys(key, n, ri)) ⊖ ro, key ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks
Proof step 27:
⊦ key0 ∈ ri ⊖ ro ∧ ¬ key0 ∈ datakeys(key, n, ri) ↔ key0 ∈ (ri \ datakeys(key, n, ri)) ⊖ ro, key ∈ ro

Rule argument

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

Additional information

Used terms: datakeys(key, n, ri), ri ⊖ ro, key0