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Proof step 16 from proof replay-orphans-del (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: at-dels-ro-nodata seq: ⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key] subst: [key, ks, ri] → [key0, ro, ri -- key] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s) Used terms: key0, ro, ri -- key